Final Exam (12/11/18)

The active ingredient in a Tylenol pill is 325 mg of acetaminophen (C₈H₉NO₂). Find the number of active molecules of acetaminophen in a single pill.

(8 moles of C)(12 grams/mole) + (9 moles H)(1 gram/mole) +(1 mole N)(14 grams/mole) + (2 moles O)(16 grams/mole) = 151 g (325 mg/151 g/mol)(1 g/1000 mg) = 2.15 x 10⁻³ N = (2.15 x 10⁻³ moles)(6.02 x 10²³ molecuels/mole) = 1.3 x 10²¹ molecules

A mass-spring system oscillates with an amplitude of 5.2 cm. If the force constant of the spring of 174 N/m and the mass is 0.39 kg, what is the magnitude of the maximum acceleration of the mass in m/s²?

(N/m)(length in m)/kg (174/0.39)(5.2/100) = 23.2 m/s²

Suppose your bicycle tire is fully inflated, with an absolute pressure of 7.00×10⁵ Pa (a gauge pressure of just under 90.0 lb/in²) at a temperature of 18.0ºC. What is the pressure after its temperature has risen to 35.0ºC? Assume that there are no appreciable leaks or changes in volume.

(P/P₀)(V/V₀) = (N/N₀)(k/k)(T/T₀) P/P₀ = T/T₀ P = P₀(T/T₀) T₀ = (18 + 273)K = 291 K T = (35 + 273)K = 308 K P = P₀(T/T₀) = (7 x 10⁵ Pa)(308 K/291 K) = 7.41 x 10⁵ Pa

Percent Relative Humidity

(Vapor density/saturation vapor density) x 100

Two blocks, A and B, are made of the same material. Block A has dimensions l×w×h = L×2L×L and Block B has dimensions 2L×2L×2L. If the temperature changes, what is (a) the change in the volume of the two blocks? (b) the change in the cross-sectional area l×w? (c) the change in the height h of the two blocks?

(a) The change in volume is proportional to the original volume. Block A has a volume of L×2L×L = 2L³. Block B has a volume of 2L×2L×2L = 8L³, which is 4 times that of Block A. Thus the change in volume of Block B should be 4 times the change in volume of Block A. (b) The change in area is proportional to the area. The cross-sectional area of Block A is L×2L = 2L², while that of Block B is 2L×2L = 4L². Because cross-sectional area of Block B is twice that of Block A, the change in the cross-sectional area of Block B is twice that of Block A. (c) The change in height is proportional to the original height. Because the original height of Block B is twice that of A, the change in the height of Block B is twice that of Block A.

Mechanical Wave

-A disturbance that is created by a vibrating object and subsequently travels through a medium from one location to another, transporting energy as it moves k = wave number (k = 2π/λ) λ = wavelength ω = 2π/T (still angular frequency) v = λ/T = λf = ω/k

Adiabatic Process

-A process in which no heat transfer takes place -No heat enters or leaves the system -∆U = -∆W

Kelvin Scale

-Absolute temperature scale -0 is the absolute lowest -Freezing point: 273.15 -Boiling point: 373.15 -Magnitude of degree K is the same as for degree C

Kilocalorie

-Amount of energy needed to change the temperature of 1 kg of water by 1° C -More commonly used than calorie

Describe the difference between overdamping, underdamping, and critical damping.

-An overdamped system moves slowly toward equilibrium -An underdamped system moves quickly to equilibrium, but will oscillate about the equilibrium point as it does so -A critically damped system moves as quickly as possible toward equilibrium without oscillating about the equilibrium

Thermal Energy

-Average tranlational kinetic energy -KE = ½mv² = 3/2kT

Sound as Pressure Waves

-Back and forth vibration of particles of the medium through which the sound wave is moving -Motion of the particles is parallel and anti-parallel to the direction of the energy transport → longitudinal

Longitudinal Wave

-Compressional wave -The disturbance is parallel to the direction of propagation

Isobaric Process

-Constant-pressure process in which a gas does work -Pressure is constant ∆W = P(V₂ -V₁) *for an ideal gas

Irreversible Process

-Depends on path -Goes in one direction

Pendulum

-Displacement from equilibrium: s=Lθ -Net force: F=-mg(sinθ) -Restoring force is NOT proportional to the displacement

What two factors affect the period of a simple harmonic oscillator?

-Force constant (k) -Mass

Celsius Scale

-Freezing point: 0 -Boiling point: 100

Fahrenheit

-Freezing point: 32 -Boiling point: 212

Overtones

-Harmonics -Multiples of the fundamental frequency

Thermal Equilibrium

-Heat flows until temperatures are equal -Established when two bodies are in contact with each other and can freely exchange energy

Convection

-Heat transfer by the macroscopic movement of a fluid -Between a surface and adjacent fluid

Second Law of Thermodynamics

-Heat transfer occupies spontaneously from higher to lower temperature bodies, but never spontaneously in the reverse direction -It is impossible in any system for heat transfer from a reservoir to completely convert to work in a cyclical process in which the system returns to its initial state.

Radiation

-Heat transfer via microwaves, infrared radiation, visible light, or another form of electromagnetic radiation being emitted or absorbed -No transfer medium required

Intensity

-I -Power unit per area -I = P/A P = power A = area

Heat of Sublimation

-L(s) -Energy required to go from a solid to vapor

Fundamental Frequency

-Lowest frequency -Longest wavelength

Nodes

-Points where the string does not move -Wave disturbance is 0 in a standing wave

PV Diagram

-Pressure vs volume -Critical point: critical temperature above which a liquid cannot exist; critical pressure: minimum pressure needed for liquid to exist

Force Constant (k)

-Related to rigidity of a system -Greater = greater restoring force; stiff system -Units: N/m

Entropy

-S -Sf = Si is reversible -Sf > Si is irreversible -Macrostates and microstates

Transverse Wave

-Shear wave -Disturbance is perpendicular to the direction of propagation

Overdamped

-System that may overshoot the equilibrium position, but will reach equilibrium over a longer period of time -Decay to equilibrium position without oscillations

Simple Harmonic Motion

-System where net force can be described by Hooke's law and no damping -T and f are independent of X -T = 2π√(k/m)

Underdamped

-System will return to equilibrium faster, but will overshoot and cross over one or more times -Frequency lowered compared to non-damped case -Amplitude decreasing with time

Period

-T -Time to complete one oscillation -Remains constant in periodic motion -Units: s or any unit of time

Macrostate

-The big picture -Macrostate with the largest multiplicity is most likely

Critical Damping

-The condition in which damping of an oscillator results in it returning as quickly as possible to its equilibrium position -Desired -Boundary solution between the two, no oscillations

Resonance

-The phenomenon of driving a system with a frequency equal to its natural frequency -Driving frequency matches natural frequency (large oscillations)

Heat

-The spontaneous transfer of energy due to a temperature difference -Form of energy -Unit: J (also cal or kcal)

Mechanical Equivalent of Heat

-The work needed to produce the same effects as heat transfer -1 kcal = 4186 J

Internal Energy

-U -Sum of kinetic and potential energies

Latent Heat Coefficients

-Unit: J/kg -Depends on the substance -Does not cause a temperature change

Isochoric (Isometric) Process

-Vertical path where volume is constant -No work is done ∆W = 0

Beat Frequency

-Wave resulting from the superposition of two similar-frequency waves has a frequency that is the average of the two -Fluctuates in amplitude (beats) -Equal to the difference in frequency between two waves -cos(2π(f₁-f₂)t)/2

Standing Wave

-Waves with the same amplitude and wavelength -Alternate between constructive and destructive interference -Interference of the incident wave and the reflected wave occurred in such a manner that there are specific points along the medium that appear to be standing still

Microstate

-Ways to get to the big picture -All are equally likely

Amplitude

-X -Maximum displacement for amplitude -Related to energy in the oscillation

Acoustic Impendance

-Z = ρv -Units: kg/(m²*s)

Intensity Reflection Coefficient

-a -Ratio of the intensity of the reflected wave relative to the incident (transmitted) wave

Specific Heat

-c -Depends on material and phase -Amount of heat necessary to change the temperature of 1 kg of mass by 1° C -Physical property -Units: J/kgK orJ/kg°C (also kcal/kg°C)

Frequency

-f -The number of events per unit time -For periodic motion, number of oscillations per unit time -Units: cycle per second (hertz-Hz)

Wave Velocity

-v(w) -The speed at which the disturbance moves -Also called propagation velocity or propagation speed

Multiplicity

-Ω -Number of internal arrangements a system can have while maintaining the same internal energy -S = (kb)ln(Ω)

Wavelength

-λ -Distance between adjacent identical parts of a wave -v(w) = λ/T -v(w) = fλ

Reflector Emissivity = _____

0

Blackbody Emissivity = _____

1

One degree on he Celsius scale is _____ times larger than one degree on the Fahrenheit scale.

1.8 180 F/100 C = 9/5

Dew Point

100% relative humidity and fog

Saturation

100% relative humidity and inhibited evaporation

A 2.5 kg block of aluminum is heated at atmospheric pressure such that its temperature increases from 18 °C to 81°C. What is the change in the internal energy (in J) of the block of aluminum? The specific heat of aluminum is 9*10² J/(kg K).

141750

A thermodynamic system undergoes a process in which its internal energy decreases by 1016 J. If at the same time 512 J of thermal energy is transferred to it, how much work (in J) is done by the system?

1528

A 1 kg block of aluminum is heated at atmospheric pressure such that its temperature increases from 22 °C to 40 °C. What is the change in the internal energy (in J) of the block of aluminum? The specific heat of aluminum is 9 x 10² J/(kg K).

16200

At 0°C, the speed of sound is.....

331 m/s

At 20°C, the speed of sound is.....

343 m/s

What is the speed of sound in air at standard temperature and pressure?

343 m/s

What is the R in the ideal gas law?

8.31 J/Kmol

A Styrofoam ice box has a total area of 0.950 m² and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned beverages at 0ºC . The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the trunk of a car at 35.0ºC ?

A = 0.95 m² d = 2.5 cm = 0.025 m T₁ = 0°C T₂ = 35°C t = 1 day = 24 hours = 86400 s Q/t = kA(T₂ - T₁)/d = ((0.01 J/s*m*°C)(0.95 m²)(35°C - 0°C))/(0.025 m) = 13.3 J/s Q = (Q/t)t = (13.3 J/s)(86400 s) = 1.15 x 10⁶ J Q = mL(f) m = Q/L(f) = (1.15 x 10⁶ J)/(334 x 10³ J/kg) = 3.44 kg

Isothermal Process

A constant-temperature process ∆U = 0 *for an ideal gas

Sonic Boom

A constructive interference of sound created by an object moving faster than sound

Carnot Cycle

A cyclical process that uses only reversible processes, the adiabatic and isothermal processes

Sound

A disturbance of matter that is transmitted from its source outward

Wave

A disturbance that moves from the place it was created

Restoring Force

A force that opposes an applied force to return an object back to equilibrium

Emissivity

A measure of how well something radiates

Greenhouse Effect

A natural phenomenon responsible for providing temperatures suitable for life on earth

Identify an object that undergoes uniform circular motion. Describe how you could trace the simple harmonic motion of this object as a wave.

A record player undergoes uniform circular motion. You could attach dowel rod to one point on the outside edge of the turntable and attach a pen to the other end of the dowel. As the record player turns, the pen will move. You can drag a long piece of paper under the pen, capturing its motion as a wave.

Resonate

A system being driven at its natural frequency

The Otto Cycle

A thermodynamic cycle, consisting of a pair of adiabatic processes and a pair of isochoric processes, that converts heat into work, e.g., the four-stroke engine cycle of intake, compression, ignition, and exhaust

Phon

A unit used to express loudness numerically

Kinetic energy is proportional to _____.

Absolute temperature

Internal energy is proportional to _____ and _____.

Absolute temperature; the number of atoms/molecules

Which is steeper line on a PV diagram: adiabatic or isothermal

Adiabatic

Specific Heat Capacity

Amount of energy necessary to raise the temperature of 1 kg of some substance by 1 degree K or C

Calorie

Amount of energy needed to change the temperature of 1 g of water by 1° C

Energy carried by a sound wave is proportional to the square of its _____.

Amplitude

Describe how amplitude is related to the loudness of a sound.

Amplitude is directly proportional to the experience of loudness. As amplitude increases, loudness increases.

Which measurement of a wave is most important when determining the wave's intensity?

Amplitude, because a wave's energy is directly proportional to its amplitude squared.

Because the disturbances add, pure constructive interference produces a wave that has twice the (Wavelength/amplitude) of the individual waves, but has the same (wavelength/amplitude).

Amplitude; wavelength

Doppler Effect

An alteration in the observed frequency of a sound due to motion of either the source or the observer

Gases (are/are not) sensitive to forces between their molecules.

Are not

The larger the value of R, the (worse/better) insulation.

Better

Reversible Process

Both the system and its environment can return to exactly the states they were in by following the reverse path

Cyclical Process

Brings a system back to its original state at the end of every cycle W = Q(h) - Q(c)

Heat (can/cannot) be converted into work.

Can

What is ∆U?

Change in internal/potential energy

Heat transferred depends on _____, _____, and _____.

Change in temperature; mass of the system; substance and its phase

A refrigerator has a coefficient of performance equal to 5.7. If the refrigerator absorbs 172 J of thermal energy from a cold reservoir in each cycle, find the work done on the system each cycle (in J).

Coefficient/energy = 172/5.7 = 30.2 J

You observe two musical instruments that you cannot identify. One plays high-pitch sounds and the other plays low-pitch sounds. How could you determine which is which without hearing either of them play?

Compare their sizes. High-pitch instruments are generally smaller than low-pitch instruments because they generate a smaller wavelength

An isobaric line on a PV diagram is _____.

Completely horizontal

Convection, Conduction, or Radiation? Lizard sitting on a rock

Conduction

Convection, Conduction, or Radiation? You are touching it

Conduction

Name an example from daily life (different from the text) for each mechanism of heat transfer.

Conduction: Heat transfers into your hands as you hold a hot cup of coffee. Convection: Heat transfers as the barista "steams" cold milk to make hot cocoa. Radiation: Reheating a cold cup of coffee in a microwave oven.

½mv² + ½kx² = _____

Constant

Convection, Conduction, or Radiation? Transmitted via fluid

Convection

Convection, Conduction, or Radiation? Wind blowing

Convection

How can a cold object transfer heat to a hot object?

Convert ordered energy to thermal energy

Thermal Stress

Created by thermal expansion or contraction

Bow Wake

Created when the wave source moves faster than the wave propagation speed

Constructive Interference

Crests of two waves are precisely aligned so they combone

Sound Pressure Level

Decibel scale based on the ratio of the pressure amplitude to a reference pressure

What are the units of β?

Decibels (dB)

Deformation

Displacement from equilibrium

Superposition

Disturbance of waves are superimposed when they come together

Why did scientist Christian Doppler observe musicians both on a moving train and also from a stationary point not on the train?

Doppler needed to compare the perception of sound when the observer is stationary and the sound source moves, as well as when the sound source and the observer are both in motion.

A nuclear power reactor has pressurized water at 300ºC . (Higher temperatures are theoretically possible but practically not, due to limitations with materials used in the reactor.) Heat transfer from this water is a complex process. Steam, produced in the steam generator, is used to drive the turbine-generators. Eventually the steam is condensed to water at 27ºC and then heated again to start the cycle over. Calculate the maximum theoretical efficiency for a heat engine operating between these two temperatures.

Eff = 1 - (T(c)/T(h) = 1 - (300 K)/(573 K) = 0.476 = 47.6%

Carnot Efficiency

Eff = 1 - (T(c)/T(h)) The maximum theoretical efficiency for a heat engine

Potential Energy of a Spring

Elastic potential energy

What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0-kg person gets in?

F = -kx k = -F/x = -(784 N/(-1.2 x 10⁻² m)) = 6.53 x 10⁴ N/m

Hooke's Law

F = restoring force x = displacement k = constant

True or false: adding heat always increases temperature.

False

Two flutists are tuning up. If the conductor hears the beat frequency increasing, are the two flute frequencies getting closer together or farther apart?

Farther apart

Coefficient of Performance

For a heat pump, it is the ratio of heat transfer at the output (the hot reservoir) to the work supplied; for a refrigerator or air conditioner, it is the ratio of heat transfer from the cold reservoir to the work supplied

Why are completely undamped harmonic oscillators so rare?

Friction often comes into play whenever an object is moving. Friction causes damping in a harmonic oscillator.

Simple Pendulum

Has an object that has a small mass that is suspended from a light wire or string

What is ∆Q?

Heat added to the system

Two samples (A and B) of the same substance are kept in a lab. Someone adds 10 kilojoules (kJ) of heat to one sample, while 10 kJ of work is done on the other sample. How can you tell to which sample the heat was added?

Heat and work both change the internal energy of the substance. However, the properties of the sample only depend on the internal energy so that it is impossible to tell whether heat was added to sample A or B.

Conduction

Heat transfer through stationary matter by physical contact

What is the maximum coefficient of performance of a heat pump that takes heat from outdoors at a temperature of -13.4 °C and delivers it indoors at a temperature of 18.1 °C.

Hot/(hot/cold) = (291.25 K/(291.25 K - 259.75 K) = 9.3

When you bring two objects of different temperature together, energy will always be transferred from the (cooler/hotter) to the (cooler/hotter) object.

Hotter to cooler

Intensity of a Soundwave

I = (∆p)²/2ρv(w)

Describe a situation in your life when you might rely on the Doppler shift to help you either while driving a car or walking near traffic.

If I am driving and I hear Doppler shift in an ambulance siren, I would be able to tell when it was getting closer and also if it has passed by. This would help me to know whether I needed to pull over and let the ambulance through.

Zeroth Law of Thermodynamics

If two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C.

Why is it important to differentiate between longitudinal and transverse waves?

In the different types of waves, energy can propagate in a different direction relative to the motion of the wave. This is important to understand how different types of waves affect the materials around them.

A gas, confined to an insulated cylinder, is compressed adiabatically (and reversibly) to half its original volume. Does the entropy of the gas increase, decrease, or remain unchanged during this process?

It remains unchanged

Why is critical damping preferred?

It returns to equilibrium rapidly and remains there

The average person produces heat at the rate of about 120 W when at rest. At what rate must water evaporate from the body to get rid of all this energy? (This evaporation might occur when a person is sitting in the shade and surrounding temperatures are the same as skin temperature, eliminating heat transfer by other methods.)

L(v) = 2430 kJ/kg = 2430 J/g m/t = (120 J/s)/(2430 J/g) = 0.0494 g/s = 2.96 g/min

Convection is driven by _____.

Large-scale flow of matter

The (smaller/larger) the temperature difference between hot and cold, the larger the fraction of heat you can divert and transform into (temperature/work).

Larger; work

Antinode

Location of maximum amplitude in standing waves

How are sound levels (β) are measured?

Logarithmic scale β = 10log₁₀(I/I₀) I₀ = 10⁻¹² W/m² = intensity → multiply by 10 to add another 10 dB to the sound level

More mass means a (shorter/longer).

Longer

Ideal gas law works for gases of (low/high) densities.

Low

Heat is proportional to _____ and _____.

Mass of the substance; temperature change

In linear expansion, α depends on the _____.

Material

Why does a wood porch feel warmer than a metal pole on a cold winter morning despite them being the same temperature?

Metal conducts heat away from your body faster than the woof does

Periodic Motion

Motion that repeats itself at regular time intervals

Is it possible to cool down a well insulated room on a hot summer day by leaving the refrigerator door open, and using the refrigerator as an air conditioner?

No

Are ultrasound and infrasound imperceptible to all hearing organisms? Explain your answer.

No, the range of perceptible sound is based in the range of human hearing. Many other organisms perceive either infrasound or ultrasound

Does the temperature of a body depend on its size?

No, the system can be divided into smaller parts each of which is at the same temperature. We say that the temperature is an intensive quantity. Intensive quantities are independent of size.

Define nodes and antinodes.

Nodes are areas of wave interference where there is no motion. Antinodes are areas of wave interference where the motion is at its maximum point.

Energy involved in a phase change depends on _____ and _____.

Number of bonds; strength of bonds

What is N?

Number of particles that make up a system

Why does a hot humid day feel warmer than a hot dry day?

On a humid day, sweat does not evaporate from the skin as efficiently as it does on dry days (evaporation of sweat cools us off)

Assume that a naked human body has a surface area of 1.5 m² and a surface temperature of 32° C. If the surrounding are at a temperature of 16° C, calculate the net rate of heat loss by the body due to radiation. Assume an emissivity of 1.

P = εσAT⁴ 146 W

Kinetic Theory

PV = 1/3Nmv² P = pressure V = volume N = number of molecules m = mass v² = average speed squared

Ideal Gas Law

PV = NkT P = pressure V = volume N = number of atoms and molecules T = temperature k = Boltzmann constant (1.38 x 10⁻²³ J/K)

5 moles of a monatomic gas has its pressure increased from 10⁵ Pa to 2 x 10⁵ Pa. This process occurs at a constant volume of 0.1 m³. Determine the change in the internal energy of the gas. a. 10⁴ J b. 15000 J c. 7500 J d. The change in U depends on how the temperature was raised

PV = nRT U = (3/2)nRT R = 8.31 J/K b. 15000 J

In a (longitudinal/transverse) wave, the particle displacement moves parallel to the energy transport.

Parallel

Notes

Particular sounds that can be produced by most instruments

Pitch

Perception of frequency v(w) = ƒλ

Loudness

Perception of intensity

Hearing

Perception of sound

∆Q and ∆W (are/are not) physical properties of a system changing from state 1 to state 2.

Physical properties

Sound is a _____ wave.

Pressure

What formula tells how much heat is required to change a phase?

Q = mL m = mass L = heat of fusion or vaporization

What formula tells how much heat is required to change a temperature?

Q = mc∆T

Quantitative Relationship Between Heat Transfer and Temperature Change

Q = mc∆T Q = heat transfer m = mass c = specific heat ∆T = change in temperature

Net Rate of Heat Transfer by Radiation

Q(net)/t = σeA(T₂⁴ - T₁⁴)

Rate of Conductive Heat Transfer

Q/t = the rate of heat transfer (watts or kcal/s) k = thermal conductivity A = surface area d = surface thickness T₂ - T₁ = temperature difference

Stefan-Boltzmann Law of Radiation

Q/t = σeAT⁴ σ = 5.67 x 10⁻⁸ J/s*m²*K⁴ e = emissivity A = surface area T absolute temperature in K

The Reaumur scale is a temperature scale that was used widely in Europe in the 18th and 19th centuries. On the Reaumur temperature scale, the freezing point of water is 0ºR and the boiling temperature is 80ºR. If "room temperature" is 25ºC on the Celsius scale, what is it on the Reaumur scale?

R = (0.8°R/°C)C = (0.8°R/°C)25°C = 20°R

Ideal Gas Law in Terms of Moles

R = 1.99 cal/mol*K R = 0.0821 L*atm/mol*K

Convection, Conduction, or Radiation? Emanating in every direction from a source

Radiation

Convection, Conduction, or Radiation? Sunlight

Radiation

R Factor

Ratio of d/k

Describe how noise-canceling headphones differ from standard headphones used to block outside sounds.

Regular headphones only block sound waves with a physical barrier. Noise-canceling headphones use destructive interference to reduce the loudness of outside sounds

Larger force constant (more stiffness) means faster vibration and (shorter/longer) periods.

Shorter

Why does snow remain on mountain slopes even when daytime temperatures are higher than the freezing temperature?

Snow is formed from ice crystals and thus is the solid phase of water. Because enormous heat is necessary for phase changes, it takes a certain amount of time for this heat to be accumulated from the air, even if the air is above 0ºC. The warmer the air is, the faster this heat exchange occurs and the faster the snow melts.

Sublimation

Solid to vapor

Imagine you observe two fireworks explode. You hear the explosion of one as soon as you see it. However, you see the other firework for several milliseconds before you hear the explosion. Explain why this is so.

Sound and light both travel at definite speeds. The speed of sound is slower than the speed of light. The first firework is probably very close by, so the speed difference is not noticeable. The second firework is farther away, so the light arrives at your eyes noticeably sooner than the sound wave arrives at your ears.

Infrasound

Sound below 20 Hz

Ultrasound

Sounds above 20,000 Hz

Engines in PV Diagrams

Start at one point in the PV diagram and return to the same point

Physical properties depend only on the _____, not on the was the system was put into this state.

State of the system

Carnot Engine

Stated in terms of reversible processes, the second law of thermodynamics has a third form: A Carnot engine operating between two given temperatures has the greatest possible efficiency of any heat engine operating between these two temperatures. Furthermore, all engines employing only reversible processes have this same maximum efficiency when operating between the same given temperatures.

An isochoritc line on a PV diagram is _____.

Straight up and down

How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is. Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.

T = 0° C = 273 K P = 1.01 x 10⁵ Pa V = 1 m³ k = 1.38 x 10⁻²³ J/K PV = NkT N = PV/kT = (1.01 x 10⁵ Pa)(1 m³)/(1.38 x 10⁻²³ J/K)(273 K) = 2.68 x 10²⁵ molecules

What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s?

T = 2π√(L/g) g = 4π²(L/T²) = 4π²(0.75 m/(1.7357 s²)) = 9.8281 m/s²

What is the period (in s) of a simple pendulum of length 0.59 m and mass 0.27 kg near the surface of a planet where the gravitational acceleration is 7.5 m/s²?

T = 2π√(L/g) = 2π√(0.59/7.5) = 1.76 m/s²

Relative Humidity

Tells how much water vapor is in the air compared with the maximum possible

U is proportional to _____.

Temperature of the system

The amount of water vapor depends on _____ and _____.

Temperature; vapor pressure

Doppler Shift

The actual change in frequency due to relative motion of source and observer

For a closed process, total work performed is _____.

The area inside

Where is work on a PV diagram?

The area underneath the line between two points W = P∆V

Thermal Expansion

The change in size or volume of a given mass with temperature due to an increase in temperature (a.k.a kinetic energy) ∆L = change in length α = coefficient of linear expansion ∆T = change in temperature

Natural Frequency

The frequency at which a system would oscillate if there were no driving and no damping force

If 25 kJ is necessary to raise the temperature of a block from 25ºC to 30ºC, how much heat is necessary to heat the block from 45ºC to 50ºC?

The heat transfer depends only on the temperature difference. Since the temperature differences are the same in both cases, the same 25 kJ is necessary in the second case.

Explain why a cup of water (or soda) with ice cubes stays at 0ºC, even on a hot summer day.

The ice and liquid water are in thermal equilibrium, so that the temperature stays at the freezing temperature as long as ice remains in the liquid. (Once all of the ice melts, the water temperature will start to rise.)

An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg. Pendulum 2 has a bob with a mass of 100 kg. Describe how the motion of the pendula will differ if the bobs are both displaced by 12º.

The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. The pendula are only affected by the period (which is related to the pendulum's length) and by the acceleration due to gravity.

A famous magic trick involves a performer singing a note toward a crystal glass until the glass shatters. Explain why the trick works in terms of resonance and natural frequency.

The performer must be singing a note that corresponds to the natural frequency of the glass. As the sound wave is directed at the glass, the glass responds by resonating at the same frequency as the sound wave. With enough energy introduced into the system, the glass begins to vibrate and eventually shatters.

Partial Pressure

The pressure a gas would create if it occupied the total volume available

Vapor Pressure

The pressure where gas coexists with its solid or liquid phase

What is the change in the rate of the radiated heat by a body at the temperature T1 = 20ºC compared to when the body is at the temperature T2 = 40ºC ?

The radiated heat is proportional to the fourth power of the absolute temperature. Because T1 = 293 K and T2 = 313 K, the rate of heat transfer increases by about 30 percent of the original rate.

Imagine you are holding one end of a jump rope, and your friend holds the other. If your friend holds her end still, you can move your end up and down, creating a transverse wave. If your friend then begins to move her end up and down, generating a wave in the opposite direction, what resultant wave forms would you expect to see in the jump rope?

The rope would alternate between having waves with amplitudes two times the original amplitude and reaching equilibrium with no amplitude at all. The wavelengths will result in both constructive and destructive interference

Why does it hurt more if your hand is snapped with a ruler than with a loose spring, even if the displacement of each system is equal?

The ruler is a stiffer system, which carries greater force for the same amount of displacement. The ruler snaps your hand with greater force, which hurts more.

Dalton's Law of Partial Pressures

The total pressure is the sum of partial pressures of the component gases, assuming ideal gas behavior and no chemical reactions between the components

In a (longitudinal/transverse) wave, the particle displacement perpendicular to the energy transport.

Transverse

True or false: it is possible for heat to flow across vacuum

True

True or false: There is not temperature change during a phase change. Why?

True Heat transfer; bonds need to be broken via energy

Measure the frequency or period of a 0.1 kg mass oscillating on a spring. What is the spring constant of this spring? a. ~0.3 N/m b. ~0.9 N/m c. ~3 N/m d. ~9 N/m e. ~80 N/m

T²/4π² = m/k c. ~3 N/m

What is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is 22.0ºC . The person has a normal skin temperature of 33.0ºC and a surface area of 1.50 m². The emissivity of skin is 0.97 in the infrared, where the radiation takes place.

T₂ = 296 K T₁ = 306 K Q(net)/t = σeA(T₂⁴ - T₁⁴) = (5.67 x 10⁻⁸ J/s*m²*K⁴)(0.97)(1.5 m²)[(295 K)⁴ - (306 K)⁴] = -99 J/s = -99 W

Why is it possible to use ultrasound both to observe a fetus in the womb and also to destroy cancerous tumors in the body?

Ultrasound can be used medically at different intensities. Lower intensities do not cause damage and are used for medical imaging. Higher intensities can pulverize and destroy targeted substances in the body, such as tumors.

Explain why using a fan in the summer feels refreshing!

Using a fan increases the flow of air: warm air near your body is replaced by cooler air from elsewhere. Convection increases the rate of heat transfer so that moving air "feels" cooler than still air.

Energy Removal By Non-Conservative Forces

W(nc) = ∆(KE + PE) W = work by non-conservative force (damping force)

Destructive Interference

Waves are out of phase and aligned crest to trough so they cancel

Temperature

What is measured with a thermometer

When does a standing wave form for a string fixed on both ends?

When an integral number of half wavelengths fit into the length of the string

How is it possible to use a standing wave's node and antinode to determine the length of a closed-end tube?

When the tube resonates at its natural frequency, the wave's node is located at the closed end of the tube, and the antinode is located at the open end. The length of the tube is equal to one-fourth of the wavelength of this wave. Thus, if we know the wavelength of the wave, we can determine the length of the tube.

You hook up a stereo system. When you test the system, you notice that in one corner of the room, the sounds seem dull. In another area, the sounds seem excessively loud. Describe how the sound moving about the room could result in these effects.

With multiple speakers putting out sounds into the room, and these sounds bouncing off walls, there is bound to be some wave interference. In the dull areas, the interference is probably mostly destructive. In the louder areas, the interference is probably mostly constructive.

How is energy transferred into or out of a system?

Work

What is ∆W?

Work done by the system

You are observing a simple harmonic oscillator. Identify one way you could decrease the maximum velocity of the system.

You could increase the mass of the object that is oscillating.

A string is clamped at both ends and plucked so it vibrates in a standing wave between two extreme positions as shown by the dashed lines below. If the string has length L and the frequency of oscillation of this mode is f, the speed of the waves on that string is mpt3_astringis.gif a. (2/3) f L b. f L c. (3/2 )f L d. 3 f L

a. (2/3) f L

If you double the radiating surface area of a star while keeping its temperature constant, its power output increases by a factor of a. 2. b. 4. c. 8. d. 16. e. 1. It stays the same.

a. 2.

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern. The first harmonic is shown. The wavelengths of the standing wavelengths of the standing waves making up the pattern cannot be a. 400 cm b. 200 cm c. 100 cm d. 66.7 cm e. 50 cm

a. 400 cm

How much heat must be added to 0.1 kg of water at 60°C to completely convert it into steam? The latent heat of vaporization is 540 kcal/kg. a. 58 kcal b. 54 kcal c. 12 kcal d. 6 kcal e. 4 kcal

a. 58 kcal

(a) Calculate the percent relative humidity on a day when the temperature is 25.0ºC and the air contains 9.40 g of water vapor per m³. (b) What is the humidity when the air temperature is 25.0ºC and the dew point is -10.0ºC ?

a. 9.4 g/m³/23 g/m³ x 100 = 40.9% b. 2.36 g/m³/23 g/m³ x 100 = 10.3%

"Room temperature" is generally defined to be 25ºC. (a) What is room temperature in ºF ? (b) What is it in K?

a. F = (9/5)C + 32 = (9/5)(25°C) + 32 = 77°F b. K = C + 273.15 = 25°C + 273.15 = 298 K

The average intensity of sunlight on Earth's surface is about 700 W/m². (a) Calculate the amount of energy that falls on a solar collector having an area of 0.500 m² in 4.00 h. (b) What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200 times smaller than its own?

a. I = P/A = (E/t)/A E = IAt = (700 W/m²)(0.5 m²)[(4 h)(3600 s/h)] = 5.04 x 10⁶ J b. I/I' =(P'/A')/(P/A) = A/A' I' = 200I = 200(700 W/m²) = 1.4 x 10⁵ W/m²

Orange growers in Florida spray their tree with water when they expect a freeze. Why does this work? a. If a mixed phase of water and ice is present, the temperature does not drop below 0°C b. During an extended freeze, ice forms a protective layer around the plant c. This only works with hot water. The hot water melts the ice

a. If a mixed phase of water and ice is present, the temperature does not drop below 0°C

(a) What is the average kinetic energy of a gas molecule at 20.0ºC (room temperature)? (b) Find the rms speed of a nitrogen molecule (N²) at this temperature.

a. KE = 3/2kT = (3/2)(1.38 x 10⁻²³ J/K)(293 K) = 6.07 x 10⁻²¹ J b. m = (2(14.0067) x 10⁻³ kg/mol)/(6.02 x 10²³ mol⁻¹) = 4.65 x 10⁻²⁶ kg √v² = v = √(3kT/m) = √(3(1.38 x 10⁻²³ J/K)(293 K)/(4.65 x 10⁻²⁶ kg) = 511 m/s

We can use a toy gun's spring mechanism to ask and answer two simple questions: (a) How much energy is stored in the spring of a tranquilizer gun that has a force constant of 50.0 N/m and is compressed 0.150 m? (b) If you neglect friction and the mass of the spring, at what speed will a 2.00-g projectile be ejected from the gun?

a. PE = ½kx² = ½(50 N/m)(0.15 m)² = 0.563 Nm = 0.563 J b. KE = PE = ½mv² = ½kx² = 0.563 J v = (2PE/m)^½ = (2(0.563 J)/0.002 kg)^½ = 23.7 (J/kg)^½ 23.7 m/s

A simple pendulum is moved from the earth to the moon. How does it change that period of oscillations? Gravitational acceleration on the moon is 1.6 m/s² a. Period increases by √6 b. Period increases by factor of 4 c. Period decreases by √6 d. Period decreases by factor of 4 e. No change in period

a. Period increases by √6

(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system? (b) What is the change in internal energy of a system when a total of 150.00 J of heat transfer occurs out of (from) the system and 159.00 J of work is done on the system?

a. Q = 40 J - 25 J = 15 J W = 10 J - 4 J = 6 J ∆U = Q - W = 15 J - 6 J = 9 J b. Q = -150 J W = 1159 J ∆U = Q - W = -150 J - (-159 J) = 9 J

A 200 Hz sound wave has a measured wavelength of 1.675 m. Which of the following statements are true? You can choose more than one statement. a. The speed of the 200 Hz wave is ~335 m/s. b. The speed of a 400 Hz wave is ~ half that of the 200 Hz wave. c. The speed ofa 400 Hz wave is ~ twice that of the 200 Hz wave. d. The wavelength of the 400 Hz wave is ~ 80 - 85 cm.

a. The speed of the 200 Hz wave is ~335 m/s. d. The wavelength of the 400 Hz wave is ~ 80 - 85 cm.

A coal-fired power station is a huge heat engine. It uses heat transfer from burning coal to do work to turn turbines, which are used to generate electricity. In a single day, a large coal power station has 2.50 × 10¹⁴ J of heat transfer from coal and 1.48 × 10¹⁴ J of heat transfer into the environment. (a) What is the work done by the power station? (b) What is the efficiency of the power station? (c) In the combustion process, the following chemical reaction occurs: C + O₂ → CO₂. This implies that every 12 kg of coal puts 12 kg + 16 kg + 16 kg = 44 kg of carbon dioxide into the atmosphere. Assuming that 1 kg of coal can provide 2.5×10⁶ J of heat transfer upon combustion, how much CO₂ is emitted per day by this power plant?

a. W = Q(h) - Q(c) = (2.5 x 10¹⁴ J) - (1.48 x 10¹⁴ J) = 1.02 x 10¹⁴ J b. Eff = W/Q(h) = (1.02 x 10¹⁴ J)/(2.5 x 10¹⁴ J) = 0.408 = 40.8% c. (2.5 x 10¹⁴ J)/(2.5 x 10⁶ J/kg) = 1 x 10⁸ kg (1 x 10⁸ kg) x (44 kg CO₂/12 kg coal) = 3.7 x 10⁸ kg CO₂

We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let's try one example of each. (a) A medical imaging device produces ultrasound by oscillating with a period of 0.400 μs. What is the frequency of this oscillation? (b) The frequency of middle C on a typical musical instrument is 264 Hz. What is the time for one complete oscillation?

a. f = 1/T = 1/(0.4 x 10⁻⁶ s) = 2.5 x 10⁶ Hz b. T = 1/f = 1/264 Hz = 1/264 cycle/s = 3.79 x 10⁻³ s = 3.79 ms

A heat engine extracts usable work by permitting a. heat to flow from a hotter object to a colder object. b. heat to flow from a colder object to a hotter object. c. heat to undergo a complete transformation into work. d. work to undergo a complete transformation into heat. e. creating more heat than it converts.

a. heat to flow from a hotter object to a colder object.

In a mixture of hydrogen, oxygen, and nitrogen gases at a given temperature, the molecules having the greatest average speed are those of a. hydrogen. b. oxygen. c. nitrogen. d. At the same temperature they all have the same speed.

a. hydrogen.

You have an empty 20 oz. soda bottle and you blow air over the opening to excite a fundamental standing wave. Now, you slice off the bottom of the bottle (it's plastic) without changing its length very much. You blow over the opening and excite a fundamental standing wave in the bottle with its bottom end open. The frequency of the standing wave in the second case a. is higher than that in the first case. b. is lower than that in the first case. c. is the same as that in the first case. d. may be higher, lower, or the same as in the first case. It cannot be predicted from the information given. e. There is no sound is produced in the second case.

a. is higher than that in the first case.

Two objects in thermal equilibrium have the same a. temperature. b. activation energy. c. internal energy. d. mass. e. momentum.

a. temperature.

In a popular classroom demonstration, a cotton ball is placed in the bottom of a strong test tube. A plunger fits inside the tube and it makes an air-tight seal. It is then pushed down very rapidly, and the cotton flashes and burns. This happens because a. when the air gets compressed its temperature increases. b. friction between the plunger and the tube ignited the cotton. c. cotton contains a pressure-sensitive substance that burns upon impact. d. the air becomes very turbulent and air friction produces heat. e. it's one of those demos that nobody understands.

a. when the air gets compressed its temperature increases.

Find the natural frequency of vibration of the salt molecule NaCl given its effective mass of 13.9 atomic mass units and a spring constant of 100 N/m. a. ~10^13 Hz b. ~6.6*10^13 Hz c. ~4.3*10^27 Hz d. ~100 Hz e. ~0.4 Hz f. ~7 Hz

a. ~10^13 Hz

A 0.5 kg mass oscillates about the equilibrium position on a vertical spring with spring constant 10 N/m. Where is its equilibrium position measured from the unstretched spring position (without the hanging mass)? a. 0.05 m b. 0.49 m c. 0 m d. 2.04 m e. 5 m

b. 0.49 m

An ideal reversible engine takes in 5 kJ of energy via heat transferred in from a 500 K burner and exhausts heat at 300 K during each closed cycle in the PV plane. The amount of heat exhausted at 300 K each cycle is a. 5 kJ. b. 3 kJ. c. 2 kJ. d. 0 kJ (it's a closed cycle). e. Not enough information is given to answer this question.

b. 3 kJ.

Data: cice = 0.50 cal/(g oC) , cwater = 1.00 cal/(g oC), csteam = 0.48 cal/(g oC), L(ice-water) = 80 cal/g , L(water-steam) = 540 cal/g How much heat is given off if 0.5 kg of steam at 373 K is converted into ice at 273 K? a. 720 kcal b. 360 kcal c. 310 kcal d. 160 kcal e. 50 kcal

b. 360 kcal

How much heat is given off if 0.5 kg of steam at 373 K is converted into ice at 273 K? a. 720 kcal b. 360 kcal c. 310 kcal d. 160 kcal e. 50 kcal

b. 360 kcal

How much heat must be removed from a 200 g block of copper to lower its temperature from 120 °C to 60 °C? The specific heat of copper is 386 J/(kg K). a. 386 J b. 4632 J c. 23160 J d. 77.2 J e. 23160 J

b. 4632 J

The total entropy of the universe is always increasing. So, when water freezes, the entropy of the water is increasing. a. True b. False

b. False

Ten gallons of water per minute is flowing through the pipe. Which is correct: the water goes a. Fastest in the wide part of the pipe b. Fastest in the narrow part c. Same speed in narrow and wide parts

b. Fastest in the narrow part

An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude A of oscillation is doubled, how does this affect the oscillation period T and the object's maximum speed v(max)? a. T and v(max) both double. b. T remains the same and v(max) doubles. c. T and v(max) both remain the same. d. T doubles and v(max) remains the same. e. T remains the same and v(max) increases by a factor of 4.

b. T remains the same and v(max) doubles.

You fill two identical mugs with coffee, but the coffee in one mug is at a higher temperature than that in the other mug. You place the two mugs simultaneously in a microwave oven and turn it on briefly. As a result, you add 1 Joule of thermal energy to each mug. Which mug experiences the larger increase in entropy (if any)? a. The two mugs experience equal increases in entropy. b. The mug containing the colder coffee experiences the larger increase in entropy. c. The mug containing the hotter coffee experiences the larger increase in entropy. d. Neither mug experiences any increase in entropy. e. The entropy of both mugs increases, but without more information it is impossible to answer the question.

b. The mug containing the colder coffee experiences the larger increase in entropy.

A star with a surface temperature of 6000 K appears yellow in color. A star with a surface temperature of 4000 K will a. look the same. b. appear reddish on color. c. appear bluish in color. d. probably be invisible.

b. appear reddish on color.

A grandfather clock is running slow. The period of its pendulum is too long. To shorten the period and make the clock run faster, you should. a. increase the length of the pendulum. b. decrease the length of the pendulum. c. increase the mass of the pendulum bob. d. decrease the mass of the pendulum bob. e. Do nothing. The period cannot be changed.

b. decrease the length of the pendulum.

In the figure below, two point sources S1 and S2, which are in phase, emit identical sound waves of wavelength 2.0 m. If L1 = 39 m and L2 = 36 m, what type of interference occurs at point P? pt3_inthefigurebelow.gif a. constructive interference b. destructive interference c. beats d. no interference at all

b. destructive interference

The frequency of a wave increases, but the speed remains the same. What happens to the distance between two consecutive crests? a. it increases b. it decreases c. stays unchanged d. first increases, then decreases e. first decreases, then increases

b. it decreases

One tea kettle is heated directly over a stove flame and another is set upon a heavy piece of metal which is directly over a flame. After they begin to whistle, you turn off the stove. a. kettle B continues to whistle, but kettle A promptly stops b. kettle A continues to whistle, but kettle B promptly stops c. both stop whistling at about the same time

b. kettle A continues to whistle, but kettle B promptly stops

Assume we can change the equilibrium state of a system via two different processes. Assume that the initial and the final state are the same. Which of the quantities ΔU, ΔQ, ΔW, and ΔT must be the same for the two processes? a. only ΔQ and ΔW b. only ΔU and ΔT c. only ΔQ and ΔT d. only ΔU and ΔW e. ΔU, ΔQ, ΔW, and ΔT

b. only ΔU and ΔT

A large current of fluid is moving to the right in the big pipe. The current in the small pipe is moving a. to the right b. to the left c. neither way

b. to the left

While a guitar string is vibrating, you gently touch the midpoint of the string to ensure that the string does not vibrate at that point. The lowest-frequency standing wave that could be present on the string a. vibrates at the fundamental frequency. b. vibrates at twice the fundamental frequency. c. vibrates at three times the fundamental frequency. d. vibrates at four times the fundamental frequency. e. There is not enough information given to decide.

b. vibrates at twice the fundamental frequency.

Your dryer is broken, so you have to hang your wet clothes from the washing machine outside to dry. Under which conditions would your clothes dry fastest? a. when it is 50°F with 50% relative humidity b. when it is 75°F with 50% relative humidity c. they will dry at the same rate at any temperature with 50% relative humidity d. the clothes will not dry with 50% relative humidity

b. when it is 75°F with 50% relative humidity

A box with a total surface area of 1.2 m² and a wall thickness of 4 cm is made of an insulating material. A 10 W electric heater inside the box maintains the inside temperature at 15 °C above the outside temperature. What is the thermal conductivity of the insulating material in units of kcal/(s °C m)? a. 54.82 b. 0.022 c. 5.3 x 10⁻⁶ d. 93.02 e. 0.00053

c. 5.3 x 10⁻⁶

A box with a total surface area of 1.2 m² and a wall thickness of 4 cm is made of an insulating material. A 10 W electric heater inside the box maintains the inside temperature at 15 °C above the outside temperature. What is the thermal conductivity of the insulating material in units of kcal/(s °C m)? a. 54.82 b. 0.022 c. 5.3 x10⁻⁶ d. 93.02 e. 0.00053

c. 5.3 x10⁻⁶

By how much does the entropy of 100 g of water at 100 oC change if the water is very slowly converted into steam at 100 oC? The latent heat of vaporization of water is 540 kcal/kg = 2260 kJ/kg. a. There is no change since the temperature is constant. b. 22.6 kJ/K c. 606 J/K d. 0.36 J/K e. 145 J/K

c. 606 J/K

When baking a potato (white or sweet) in the oven, I find they come out much more uniformly cooked if I stick aluminum rods into the potato. (You can buy such rods in any kitchen supply store. Why does this work? a. Because the aluminum has a much higher specific heat than the potato and so it holds a lot of thermal energy. b. Because the aluminum has a much lower specific heat than the potato and so it lets the potato have most of the thermal energy. c. Because the aluminum has a much higher thermal conductivity than the potato so putting the rods in brings the thermal energy into the center of the potato more quickly so it cooks more uniformly. d. Some other reason.

c. Because the aluminum has a much higher thermal conductivity than the potato so putting the rods in brings the thermal energy into the center of the potato more quickly so it cooks more uniformly.

Which of the statements below is wrong? a. For the same amplitude and the same pendulum length, the period is independent of the mass. b. The period of a simple pendulum noticeably depends on the amplitude for large amplitudes. c. The net force acting on the pendulum bob is F = -mgsinθ. The period increases with amplitude because this force increases faster than harmonic restoring force F= -mgθ. d. A damped pendulum does not have a constant period. e. In a zero g environment a pendulum does not execute oscillatory motion.

c. The net force acting on the pendulum bob is F = -mgsinθ. The period increases with amplitude because this force increases faster than harmonic restoring force F= -mgθ.

Why does heat, of itself, not flow from a cold to a hot object, if it is allowed by Newton's laws? a. Energy would not be conserved b. Cold matter is more dense, and therefore this would require transfer of matter c. This would require a large departure from equilibrium, which is extremely unlikely d. Heat does flow from cold objects to hot objects. Every winter regions near the poles get colder while regions near the equator get even hotter

c. This would require a large departure from equilibrium, which is extremely unlikely

Can an object's velocity change direction when its acceleration is constant? a. No, this is not possible because it is always speeding up. b. No, this is not possible because it is always speeding up or always slowing down, but it can never turn around. c. Yes, this is possible, and a rock thrown straight up is an example. d. Yes, this is possible, and a car that starts from rest, speeds up, slows to a stop, and then backs up is an example. e. Yes, this is possible, but then the net force must change direction.

c. Yes, this is possible, and a rock thrown straight up is an example.

In any process, the maximum amount of heat that can be converted into mechanical energy a. depends on whether kinetic or potential energy is involved. b. depends only on the amount of friction present. c. depends on the intake and exhaust temperatures. d. is 100%.

c. depends on the intake and exhaust temperatures.

A pitcher contains 0.5 kg of liquid water and 0.5 kg of ice at 0°C. You let heat flow into the pitcher until there is 0.75 kg of liquid water and 0.25 kg of ice. During this process, a. the temperature of the ice-water mixture increases slightly b. the temperature of the ice-water mixture decreases slightly c. the temperature of the ice-water mixture remains the same d. the answer depends on the rate at which heat flows

c. the temperature of the ice-water mixture remains the same

The liquid level in a glass thermometer rises as the temperature increases because a. the pressure in the thermometer decreases. b. the volume expansion coefficient of glass is greater than that of the liquid. c. the volume expansion coefficient of glass is less than that of the liquid. d. the volume expansion coefficient of glass is the same as that of the liquid. e. the pressure in the thermometer increases.

c. the volume expansion coefficient of glass is less than that of the liquid.

If you double the wavelength of a wave on a string under fixed tension, what happens to the wave speed, v, and the wave frequency, f? a. both are doubled b. v is doubled and f is unchanged c. v is unchanged and f is halved d. v is unchanged and f is doubled e. v is halved and f is unchanged

c. v is unchanged and f is halved

An object with mass m moves through free space with constant velocity. The magnitude of the force required to maintain this motion is equal to a. the mass of the object m. b. mg. c. zero. d. the force required to stop it.

c. zero.

Water is boiling in an aluminum pan placed on an electrical element on a stovetop. The sauce pan has a bottom that is 0.800 cm thick and 14.0 cm in diameter. The boiling water is evaporating at the rate of 1.00 g/s. What is the temperature difference across (through) the bottom of the pan?

d = 0.8 cm = 8 x 10⁻³ m A = π(0.14/2)² m² = 1.54 x 10⁻² m² k = 220 J/s*m*°C Q = mL(v) = (1 x 10⁻³ kg)(2256 x 10³ J/kg) = 2256 J Q/t = 2256 J/s (2.26 kW) T₂ - T₁ = (Q/t)(d/kA) = (2256 J/s)((8 x 10⁻³ m)/((220 J/s*m*°C)(1.54 x 10⁻² m²))) = 5.33°C`

The intensity of sound wave A is 100 times that of sound wave B. Relative to wave B the sound level of wave A is a. -2 dB. b. +2 dB. c. +10 dB. d. +20 dB. e. +100 dB.

d. +20 dB.

A point source of sound waves emits a disturbance with a power of 50 W = 50 J/s into a surrounding homogeneous medium. What is the intensity of the sound at a distance of 10 m from the source? a. 5 W/m2 b. 0.5 W/m2 c. 0.08 W/m2 d. 0.04 W/m2 e. 0.4 W/m2

d. 0.04 W/m2

A ball is thrown directly downward with an initial speed of 8 m/s from a height of 30 m. After what time interval does the ball strike the ground? a. 3.75 s b. 6.1 s c. 2.47 s d. 1.78 s e. 1.23 s

d. 1.78 s

If the intensity of a 40 dB sound is increased to 80 dB, the intensity in W/m² increases by a factor of a. 1 b. 4 c. 40 d. 10⁴ c. 100⁵

d. 10⁴ β = 10log₁₀(I/I₀)

Two dice are thrown. Let the macrostate be the sum of the two numbers on the top faces. What is the multiplicity of the macrostate "4"? a. 4 b. 6 c. 2 d. 3 e. 1

d. 3

At which of the following temperatures would molecules have twice the average kinetic energy they have at room temperature, 20 °C? a. 40 °C b. 68 °C c. 80 °C d. 313 °C e. 586 °C

d. 313 °C

Ethyl alcohol boils at 172 °F. What is Celsius equivalent of this temperature? a. 451 °C b. 278 °C c. 140 °C d. 78 °C e. 64 °C

d. 78 °C

pt3_pressure.gif Pressure vs. volume graphs for a certain gas undergoing five different cyclic processes are shown to the right. During which cycle does the gas do the greatest positive work? a. I b. II c. III d. IV e. V

d. IV

Fall Sem 2018 Home Announcements Assignments Discussions Grades2 People Files Syllabus Quizzes Modules Collaborations Chat myUTK Badges Google Drive Office 365 More practice problems 3 Due No due date Points 23 Questions 23 Available until Dec 14 at 11:59pm Time Limit None Allowed Attempts Unlimited Instructions This practice test allows multiple attempts. No score is kept. Test 3 is a 1 hour and 20 minutes test. There are 23 problems. You can omit 3 problems. The highest score you can get is 20/20. Oscillations and Waves: Harmonic motion: F = -kx. x(t) = Acos(ωt + φ), v(t) = -ωAsin(ωt + φ), a(t) = -ω2Acos(ωt + φ) = -ω2x. ω = sqrt(k/m) = 2πf = 2π/T. Pendulum: T = 2π(L/g)1/2 Traveling waves: y(x,t) = A sin(kx - ωt ± φ) Waves on a string: v = (F/μ)1/2 Sound level: β = 10 log10(I/I0) Beat frequency: |f1 - f2| Standing sound waves: tube of length L with two open ends: L = nλ/2, n = 1, 2, 3, ... tube of length L with one open end and one closed: L = nλ/4, n = odd integer Doppler effect: f = f0(v - vobs)/(v - vs) (velocity components in the direction of v are positive) Temperature and Heat Ideal gas: PV = (2/3)N(m<v2>/2) = (2/3)U, PV = NkBT = nRT kB = 1.381*10-23 J/K, R = 8.31 J/(mol K) Linear expansion: ΔL = αLΔT Thermal conductivity: ΔQ/Δt = -kA ΔT/Δx Stefan-Boltzmann Law: Radiated power = emissivity * σ * T4 * Area Wien Law: λmax(nm) = 3*106/T(K) Specific heat: c = ΔQ/(m ΔT) Latent heat: ΔQ = mL Thermodynamics: First law: ΔU = ΔQ - ΔW Second law: Qhigh/Thigh = Qlow/Tlow Entropy: S = kB lnΩ, ΔS = ΔQ/T Conversion: Cal = 1 kcal = 4186 J Attempt History Attempt Time Score KEPT Attempt 5 1 minute 21 out of 23 LATEST Attempt 5 1 minute 21 out of 23 Attempt 4 2 minutes 20 out of 23 Attempt 3 3 minutes 18 out of 23 Attempt 2 4 minutes 18 out of 23 Attempt 1 7 minutes 8 out of 23 Correct answers are hidden. Score for this attempt: 21 out of 23 Submitted Dec 11 at 2:01pm This attempt took 1 minute. Question 1 1 / 1 pts Data: cice = 0.50 cal/(g oC) , cwater = 1.00 cal/(g oC), csteam = 0.48 cal/(g oC), L(ice-water) = 80 cal/g , L(water-steam) = 540 cal/g Which requires the most energy? Raise the temperature of 1 gram of liquid water by 50 oC. Melt 1 gram of ice at T = 0 oC. Raise the temperature of 1 gram of ice from 73K to 273K. Vaporize 0.5 gram of water at T = 100 oC. Correct! Question 2 1 / 1 pts Ethyl alcohol boils at 172 oF. What is Celsius equivalent of this temperature? 451 oC 278 oC 140 oC 78 oC 64 oC Correct! Question 3 1 / 1 pts Data: cice = 0.50 cal/(g oC) , cwater = 1.00 cal/(g oC), csteam = 0.48 cal/(g oC), L(ice-water) = 80 cal/g , L(water-steam) = 540 cal/g How much heat is given off if 0.5 kg of steam at 373 K is converted into ice at 273 K? 720 kcal 360 kcal 310 kcal 160 kcal 50 kcal Correct! Question 4 1 / 1 pts In a popular classroom demonstration, a cotton ball is placed in the bottom of a strong test tube. A plunger fits inside the tube and it makes an air-tight seal. It is then pushed down very rapidly, and the cotton flashes and burns. This happens because when the air gets compressed its temperature increases. friction between the plunger and the tube ignited the cotton. cotton contains a pressure-sensitive substance that burns upon impact. the air becomes very turbulent and air friction produces heat. it's one of those demos that nobody understands. Correct! Question 5 1 / 1 pts The liquid level in a glass thermometer rises as the temperature increases because the pressure in the thermometer decreases. the volume expansion coefficient of glass is greater than that of the liquid. the volume expansion coefficient of glass is less than that of the liquid. the volume expansion coefficient of glass is the same as that of the liquid. the pressure in the thermometer increases. Correct! Question 6 1 / 1 pts By how much does the entropy of 100 g of water at 100 oC change if the water is very slowly converted into steam at 100 oC? The latent heat of vaporization of water is 540 kcal/kg = 2260 kJ/kg. There is no change since the temperature is constant. 22.6 kJ/K 606 J/K 0.36 J/K 145 J/K Correct! Question 7 1 / 1 pts The maintenance of the life cycle depends on the presence of a source and a sink of energy. the decrease of the entropy of the universe. the fact that organisms higher on the food chain are more organized. the fact that a living organism is a highly probably state. the fact that thermodynamics cannot be applied to the biological systems. Correct! IncorrectQuestion 8 0 / 1 pts The specific heat of aluminum is 0.215 kcal/(kgoC). A 3 kg block of aluminum is heated from 10oC to 150oC. What is the change in the internal energy (in units of kcal) of the block? Enter an integer. 9030 Incorrect! ΔQ = c m ΔT, ΔW = 0 since the aluminum does no work. Use the first law of thermodynamics. Question 9 1 / 1 pts The total entropy of the universe is always increasing. So, when water freezes, the entropy of the water is increasing. True False Correct! IncorrectQuestion 10 0 / 1 pts A car travels over a dirt road that contains a series of equally spaced bumps (a so-called "washboard" road). While traveling at a given speed the driver experiences a very jarring ride. When the driver drives at a higher speed, however, the ride gets smoother. That is because the car actually leaves the ground at higher speeds. the faster moving car actually crushes the bumps and makes the road smoother. the car's shock absorbers have more friction at higher speeds. at the higher speed more of the up and down motion is converted into forward motion. going faster in the car forces the suspension to oscillate at a frequency higher than its natural frequency. Incorrect! Review driven oscillations! What is the condition for resonance to occur? Question 11 1 / 1 pts A string is clamped at both ends and plucked so it vibrates in a standing wave between two extreme positions as shown by the dashed lines below. If the string has length L and the frequency of oscillation of this mode is f, the speed of the waves on that string is mpt3_astringis.gif (2/3) f L f L (3/2 )f L 3 f L Correct! Question 12 1 / 1 pts Find the natural frequency of vibration of the salt molecule NaCl given its effective mass of 13.9 atomic mass units and a spring constant of 100 N/m. ~1013 Hz ~6.6*1013 Hz ~4.3*1027 Hz ~100 Hz ~0.4 Hz ~7 Hz Correct! Question 13 1 / 1 pts In simple harmonic motion the magnitude of the velocity is greatest at the maximum displacement. the period depends on the amplitude. the acceleration is constant. the magnitude of the acceleration is greatest at zero displacement. none of the above. Correct! Question 14 1 / 1 pts You have an empty 20 oz. soda bottle and you blow air over the opening to excite a fundamental standing wave. Now, you slice off the bottom of the bottle (it's plastic) without changing its length very much. You blow over the opening and excite a fundamental standing wave in the bottle with its bottom end open. The frequency of the standing wave in the second case is higher than that in the first case. is lower than that in the first case. is the same as that in the first case. may be higher, lower, or the same as in the first case. It cannot be predicted from the information given. There is no sound is produced in the second case. Correct! Question 15 1 / 1 pts The Doppler effect is characteristic of water waves. sound waves. light waves. all of the above choices. none of the above choices. Correct! Question 16 1 / 1 pts In the figures (a), (b), (c), (d) and (e) below, S is a source of sound of real frequency f and L is a listener. The speeds of the source and the listener are equal (v) in all cases except in (e) where the source is at rest and the listener is moving with speed v (as in the other cases). There is no wind. From the statements below, pick out the wrong statement. mpt3_inthefigures.gif a. In the case shown in figure (a) the apparent frequency as heard by the listener is equal to the real frequency of the source. b. In the case shown in fig (b) the apparent frequency as heard by the listener is the greatest. c. In the case shown in fig (c) the apparent frequency as heard by the listener is the least. d. In the case shown in fig (d) the apparent frequency as heard by the listener is less than the real frequency of the source e. In the case shown in fig (e) the apparent frequency as heard by the listener is greater than the real frequency of the source

d. In the case shown in fig (d) the apparent frequency as heard by the listener is less than the real frequency of the source

A car's speed changes from 20 mph to 60 mph. By what factor does its kinetic energy change? a. There is no way to tell. b. It will increase by a factor of 3. c. It will increase by a factor of 6. d. It will increase by a factor of 9. e. It will stay constant.

d. It will increase by a factor of 9.

On a humid summer day, perspiration does not cool you off much. Why? a. The air density is extremely low and the air pressure is too high to permit water to evaporate. b. The water vapor in the air is moving too fast to condense on your skin as perspiration. c. The air density is extremely low and its pressure is too low to permit water to evaporate. d. The air is almost saturated with water vapor and there is almost no net evaporation.

d. The air is almost saturated with water vapor and there is almost no net evaporation.

A chair has a wooden seat but metal legs. The chair legs feel colder to the touch than the seat does. Why? a. The metal is at a lower temperature than the wood b. The metal has a higher specific heat than the wood c. The metal has a lower specific heat than the wood d. The metal has a higher thermal conductivity than the wood e. The metal has a lower thermal conductivity than the wood

d. The metal has a higher thermal conductivity than the wood

Data: c(ice) = 0.50 cal/(g °C) , c(water) = 1.00 cal/(g °C), c(steam) = 0.48 cal/(g °C), L(ice-water) = 80 cal/g L(water-steam) = 540 cal/g Which requires the most energy? a. Raise the temperature of 1 gram of liquid water by 50 °C. b. Melt 1 gram of ice at T = 0 °C. c. Raise the temperature of 1 gram of ice from 73K to 273K. d. Vaporize 0.5 gram of water at T = 100 °C.

d. Vaporize 0.5 gram of water at T = 100 °C.

The Doppler effect is characteristic of a. water waves. b. sound waves. c. light waves. d. all of the above choices. e. none of the above choices.

d. all of the above choices.

A car travels over a dirt road that contains a series of equally spaced bumps (a so-called "washboard" road). While traveling at a given speed the driver experiences a very jarring ride. When the driver drives at a higher speed, however, the ride gets smoother. That is because a. the car actually leaves the ground at higher speeds. b. the faster moving car actually crushes the bumps and makes the road smoother. c. the car's shock absorbers have more friction at higher speeds. d. at the higher speed more of the up and down motion is converted into forward motion. e. going faster in the car forces the suspension to oscillate at a frequency higher than its natural frequency.

d. at the higher speed more of the up and down motion is converted into forward motion.

Living cells constitute a low entropy state of matter. Living cells a. violate the second law of thermodynamics. b. demonstrate that the laws of thermodynamics are incomplete. c. are not subject to physical laws such as thermodynamics. d. can exist because they help increase the entropy of the rest of the universe. e. violate the first law of thermodynamics.

d. can exist because they help increase the entropy of the rest of the universe.

In any process, the maximum amount of mechanical energy that can be converted into thermal energy a. depends on the intake and exhaust temperatures. b. depends on whether kinetic or potential energy is involved. c. depends only on the amount of friction present. d. is 100%. e. is less than 80%.

d. is 100%.

A string is clamped at both ends and then plucked so that it vibrates in a standing mode between two extreme positions a and c. Let upward motion correspond to positive velocities. When the string is in position b, the instantaneous velocity of points along the string pt3_astringis.gif a. is zero everywhere. b. is positive everywhere. c. is negative everywhere. d. is zero, positive, or negative, depending on the position along the string.

d. is zero, positive, or negative, depending on the position along the string.

You are watching a semi truck bounce up and down on a spring. (Yep it's a toy.) At the topmost point in the truck's path, a. the truck's velocity is downward but its acceleration is upward. b. the truck's velocity is zero but its acceleration is upward. c. the truck's velocity is upward but its acceleration is downward. d. the truck's velocity is zero but its acceleration is downward. e. the truck's velocity is downward and its acceleration is downward.

d. the truck's velocity is zero but its acceleration is downward.

The temperature in a furnace used to melt Aluminum is 660 °C. What is the average kinetic energy of the air molecules in the furnace? a. 660 J b. 9 x 10⁻²¹ J c. 933 J d. 1.37 x 10⁻²⁰ J e. 1.93 x 10⁻²⁰ J

e. 1.93 x 10⁻²⁰ J

The temperature on a nice summer day is 84 °F. What is the temperature on the absolute (Kelvin) temperature scale? a. 456 K b. 29 K c. 357 K d. 187 K e. 302 K

e. 302 K

The illustration shows a thermometer that uses a column of liquid to measure air temperature. In thermal equilibrium, this thermometer measures the temperature of a. the column of liquid only. b. the glass that encloses the liquid only. c. the air outside the thermometer only. d. the liquid and the glass only. e. all of the above.

e. all of the above.

Which sounds travel the fastest through air? a. higher pitch sound b. lower pitch sound c. louder sound d. quieter sound e. all sound travels at the same speed through air

e. all sound travels at the same speed through air

In the figure, student a has a mass of 95 kg and student b has a mass of 77 kg. They sit in identical office chairs facing each other. Student a places his bare feet on the knees of student b, as shown. Student a then suddenly pushes outward with his feet, causing both chairs to move. During the push, and while the students are still touching one another mpt3_inthefigure_push.gif a. neither student exerts a force on the other. b. student a exerts a force on student b, but student b does not exert a force on student a. c. each student exerts a force on the other, but student b exerts the larger force. d. each student exerts a force on the other, but student a exerts the larger force. e. each student exerts the same amount of force on the other.

e. each student exerts the same amount of force on the other.

In simple harmonic motion a. the magnitude of the velocity is greatest at the maximum displacement. b. the period depends on the amplitude. c. the acceleration is constant. d. the magnitude of the acceleration is greatest at zero displacement. e. none of the above.

e. none of the above.

A hypothetical engine operates in a cycle taking in 10,000 J from a hot reservoir and 5000 J from a cold reservoir. In the cycle it performs 15,000 J of work. Such an engine a. obeys both the first and second laws of thermodynamics. b. violates both the first and second laws of thermodynamics. c. violates the first law but obeys the second law of thermodynamics. d. conserves entropy. e. obeys the first law but violates the second law of thermodynamics.

e. obeys the first law but violates the second law of thermodynamics.

If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping. Calculate the frequency and period of these oscillations for such a car if the car's mass (including its load) is 900 kg and the force constant (k) of the suspension system is 6.53 ×10⁴ N/m .

f = ½π√(k/m) = ½π√((6.53 x 10⁴ N/m)/900 kg) = 1.3656/s⁻¹ = 1.36 Hz T = 1/f = 1/1.36 Hz = 0.738 s

Most houses are not airtight: air goes in and out around doors and windows, through cracks and crevices, following wiring to switches and outlets, and so on. The air in a typical house is completely replaced in less than an hour. Suppose that a moderately-sized house has inside dimensions 12.0m×18.0m×3.00m high, and that all air is replaced in 30.0 min. Calculate the heat transfer per unit time in watts needed to warm the incoming cold air by 10.0ºC, thus replacing the heat transferred by convection alone.

m = ρV = (1.29 kg/m³)(12 m x 18 m x 3 m) = 836 kg Q = mc∆T = (836 kg)(1000 J/kg°C)(10°C) = 8.36 x 10⁶ J t = 0.5 hr = 1800 s Q/t = (8.36 x 10⁶ J)/1800 s = 4.64 kW

Three ice cubes are used to chill a soda at 20ºC with mass msoda = 0.25 kg. The ice is at 0ºC and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Find the final temperature when all ice has melted.

m(ice) = 3 x 6 g = 0.018 kg m(soda) = 0.25 kg (m(soda))(c(water))(20°C) = (0.25 kg)(4186 J/kg°C)(20°C) = 20930 J (m(ice))(L(f)) = (0.018 kg)(334,000 J/kg) = 6012 J (m(soda) + m(ice))(c(water)) = (0.25 kg + 0.018 kg)(4186 K/(kg°C) = 1122 J/°C T(f) = (20930 J - 6012 J)/1122 J/°C = 13°C

How many moles of gas are in a bike tire with a volume of 2.00×10⁻³ m³(2.00 L), a pressure of 7.00×10⁵ Pa (a gauge pressure of just under 90.0 lb/in²), and at a temperature of 18.0ºC?

n = PV/RT = (7 x 10⁵ Pa)(2 x 10⁻³ m³)/(8.31 J/mol*K)(291 K) = 0.579 mol

Most gases have the same _____.

rate or β

Suppose that a car is 900 kg and has a suspension system that has a force constant k = 6.53×10⁴ N/m . The car hits a bump and bounces with an amplitude of 0.100 m. What is its maximum vertical velocity if you assume no damping occurs?

v(max) = X√(k/m) = (0.1 m)√((6.53 x 10⁴ N/m)/900 kg) = 0.852 m/s

Speed of Sound: Gases

v(rms) = √(3kT/m)

Speed of Sound: Air at Sea Level

v(w) = (331 m/s)√(T/273 K)

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0ºC air. (Assume that the frequency values are accurate to two significant figures.)

v(w) = (331 m/s)√(T/273 KM) = (331 m/s)√(303 K/273 K) = 348.7 m/s λ = v(w)/ƒ = 348.7 m/s/20 Hz = 17 m λ(min) = 348.7 m/s/20,000 Hz = 0.017 m = 1.7 cm

Calculate the wave velocity of the ocean wave if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.

v(w) = λ/T = 10 m/5 s = 2 m/s

Conservation of Energy for Simple Harmonics

½mL²ω² + ½mgLθ² = constant

Standing Waves Equation

λ = (2/n)L for wavelength n = harmonic or half waves f = v/λ for frequency

Thermal Expansion in Two Dimensions

∆A = change in area α = coefficient of linear expansion ∆T = change in temperature

The main span of San Francisco's Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from -15ºC to 40ºC . What is its change in length between these temperatures? Assume that the bridge is made entirely of steel (α = 12 x 10⁻⁶).

∆L = αL∆T = (12x10⁻⁶/°C)(1275m)(55°C) = 0.84 m

How do you calculate specific heat?

∆Q = cm∆T

How do you calculate latent heat?

∆Q = mL

Change in Entropy for an Irreversible System

∆S = S₂ - S₁

Spontaneous heat transfer from hot to cold is an irreversible process. Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at Th = 600 K(327º C) to a cold reservoir at Tc = 250 K(−23º C) , assuming there is no temperature change in either reservoir.

∆S(tot) = ∆S(h) + ∆S(c) ∆S(h) = -Q(h)/T(h) = (-4000 J/600 K) = -6.67 J/K ∆S(c) = Q(c)/T(c) = (4000 J/250 K) = 16 J/K ∆S(tot) = (-6.67 + 16) = 9.33 J/K

A 0.500 kg aluminum pan on a stove is used to heat 0.250 liters of water from 20.0ºC to 80.0ºC. (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) the pan and (c) the water? (c(water) = 4186 J/kg°C; c(aluminum) = 900 J/kg°C)

∆T = 80 - 20 = 60°C ρ(water) = 1000 kg/m³ m(water) = 0.25 kg Q(water) = mc∆T = (0.25 kg)(4186 J/kg°C)(60°C) = 62.8 kJ Q(aluminum) = mc∆T = (0.5 kg)(900 J/kg°C)(60°C) = 27 x 10⁴ J = 27 kJ Q(total) = Q(water) + Q(aluminum) = 62.8 kJ + 2 kJ = 89.8 kJ Heat going into the pan: (27 kJ/89.9 kJ) x 100 = 30.1% Heat going into the water: (62.8 kJ/89.8 kJ) x 100 = 69.9 %

First Law of Thermodynamics

∆U = change in internal energy Q = net heat transferred into the system W = net work done by the system

What pressure would be created in the gasoline tank considered, if the gasoline increases in temperature from 15.0ºC to 35.0ºC without being allowed to expand? Assume that the bulk modulus B for gasoline is 1.00×10⁹ N/m².

∆V = (1F/BA)V₀ P = F/A = (∆V/V₀)B = (1.1 L/60 L)(1 x 10⁹ Pa) = 1.83 x 10⁷ Pa

Thermal Expansion in Three Dimensions

∆V = βV∆T β = coefficient of volume expansion (β≈3α)

Suppose your 60.0-L (15.9-gal) steel gasoline tank is full of gas, so both the tank and the gasoline have a temperature of 15.0ºC. How much gasoline has spilled by the time they warm to 35.0ºC?

∆V = βV∆T V = (β - β)V∆T = [(950 - 35)x10⁻⁶/°C](60 L)(20 °C) = 1.1 L

What is the work if volume doesn't change from state A to state B?

∆W = 0

What is the work if volume changes and pressure does not?

∆W = P∆V