Physics Test 3
A sealed container contains a fixed volume of a monatomic ideal gas. If the gas temperature is increased by a factor of two, what is ratio of the final to the initial pressure, average molecular kinetic energy, root-mean-square speed, and internal energy? (Pressure)
(a) The correct answer is 2. The ideal gas law is PV = nRT. With n and V constant, pressure is proportional to temperature so that doubling the temperature results in a doubling of the pressure: Tf/Ti = Pf/Pi = 2.
what is the weight of the water displaced by a 100 ton floating ship
100 tons
(b) Repeat the question if the stars have the same radius, but star A has twice the absolute temperature of star B.
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The freezing point of pure water is 0 degrees C. Which of the following temperatures represents one that is double this based on an absolute temperature scale? 0 degrees C 100 degrees C 200 degrees C 273.15 degrees C
273.15 degrees C. Tc=Tk-273.15
Stars A and B have the same temperature, but star A has twice the radius of star B. (a) What is the ratio of star A's power output to star B's output due to electromagnetic radiation? The emissivity of both stars can be assumed to be 1.
4
first law of thermodynamics equation
Q= delta U + W
mars
thin atmosphere (1% Earths) 95% carbon dioxide
iso-volumetric
volume stays constant, vertical line on PV diagram constant volume--- no work done
Buoyant force
weight of the fluid displaced. B=pfvfg
A grandfather clock is controlled by a swinging brass pendulum that is 1.6 m long at a temperature of 26°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (Give your answer to at least four significant figures.)
(a) As the temperature drops by 26°C, the length of the pendulum changes by ΔL = αL0(ΔT) = [19 ✕ 10−6 (°C)−1](1.6 m)(−26°C) or ΔL = −7.9 ✕ 10−4 m = −0.79 mm. Thus, the final length of the rod is L = 1.6 m − 0.79 mm = 1599.2 mm.
(b) average molecular kinetic energy
(b) The correct answer is 2. The average kinetic energy per molecule is KE = 1/2mv2 = 3/2kBT. The average kinetic energy per molecule is proportional to temperature so that doubling the temperature doubles the average kinetic energy per molecule and Tf/Ti = KEf/KEi = 2.
(b)If a pendulum's period is given by T = 2πL/g, where L is its length, does the change in length of the rod cause the clock to run fast or slow?
(b) From the expression for the period, T = 2πL/g, we see that as the length decreases the period decreases. Thus, the pendulum will swing too rapidly and the clock will run fast.
(c) root-mean-square speed
(c) The correct answer is root2. The average kinetic energy per molecule is KE = 1/2mv2 = 3/2kBT so that v2 is proportional to temperature and the rms speed, v2, is proportional to the square root of the temperature. rootTf/Ti= rootKEf/KEi = rootvf2/vi2 = 2 ≈ 1.41
three ways to transfer energy
1) conduction- heat transfer through physical contact 2)convection- heat transfer through motion 3)radiation- heat transfer through photons
(c) What's the ratio if star A has both twice the radius and twice the absolute temperature of star B?
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A person shakes a sealed, insulated bottle containing coffee for a few minutes. What is the change in the temperature of the coffee? no change, a large increase, a large increase, a slight decrease, a slight increase
A slight increase
Archimedes principle
Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by that object. Can use water to find the volume of the object based on fluid displaced
Why doesn't the melting point of ocean based ice raise as much concern as the melting point of land based ice?
Because ice is less dense than water. Ice is already displacing its own weight when it is floating, so ice on land is the problem
Planets in solar system
Biggest difference is temperature. Inner planets closer to the sun is warmer and outer planets farther from the sun is colder
Archimedes principle
Buoyed up by the weight of the water displaced---two equal cups, one put in water= not equal, put the displaced water in the cup in the water= equal again
Two objects with different sizes, masses, and temperatures are placed in thermal contact. Choose the best answer. Energy travels from the larger object to the smaller object. Energy travels from the object at higher temperature to the object at lower temperature. Energy travels from the object with more mass to the one with less mass.
Energy travels from the object at higher temperature to the object at lower temperature.
T/F Atmospheric pressure increases in a tornado or hurricane
False. Pressure decreases in a tornado/hurricane because they are low pressure systems
Wien's Law
Hotter objects emit photons with a higher average energy (wavelength peak about equal to 1/T) *the hotter the star, the shorter the wavelength
Mercury, Venus, Earth, Mars
No hydrogen and helium Smaller masses such as hydrogen and helium move faster)
The three containers in the figure below are filled with water to the same level. Rank the pressures at the bottom of the containers.
PA=PB=PC. Pressure varies with fluid depth but not with the container's shape. The depth is equal in each container, so the pressures at the bottom are equal.
Kinetic gas theory
Pressure is due to particles moving around in an object. Temperature is related to average kinetic energy
Equal masses of substance A at 97.1°C and substance B at 32.2°C are placed in a well-insulated container of negligible mass and allowed to come to equilibrium. If the equilibrium temperature is 71.4°C, which substance has the larger specific heat? The answer depends on the exact initial temperatures, substance B, the specific heats are identical, substance A, more information is required.
Substance A has the higher specific heat. Substances A and B have equal masses and, from Qcold = −Qhot, an equal magnitude of energy is transferred to each. Because q = mcΔT, the sample that undergoes the lower temperature change coming to equilibrium has the higher specific heat. Substance A undergoes a 25.7°C temperature change while B undergoes a 39.2°C change.
Equal masses of substance A at 91.1°C and substance B at 12.2°C are placed in a well-insulated container of negligible mass and allowed to come to equilibrium. If the equilibrium temperature is 70.4°C, which substance has the larger specific heat? The answer depends on the exact initial temperatures, substance B, substance A, the specific heats are identical, more information is required.
Substance A has the higher specific heat. Substances A and B have equal masses and, from Qcold = −Qhot, an equal magnitude of energy is transferred to each. Because Q = mcΔT, the sample that undergoes the lower temperature change coming to equilibrium has the higher specific heat. Substance A undergoes a 20.7°C temperature change while B undergoes a 58.2°C change.
Changing direction of vector quantity
System responds. Ex: Donald holds the wheel and moves it around while spinning, which makes him turn on chair
kelvin temperature scale
Tc=Tk-273.15 (the size of the degree in kelvin scale is the same as the size of a celcius degree) The kelvin temperature scale defines "Absolute Zero"
Which one of the following statements is true? The path on a PV diagram always goes from the smaller volume to the larger volume, the area under the path on a PV diagram is always equal to the work done on a gas, the path on a PV diagram always goes from the smaller pressure to the larger pressure, the area under the path on a PV diagram is always equal in magnitude to the work done on a gas.
The area under the path on a PV diagram is always equal in magnitude to the work done on a gas. The work done on a gas is positive when the gas is compressed to smaller volumes and is negative when the gas expands to larger volumes.
(d) internal energy
The correct answer is 2. The internal energy of a monatomic gas is U = 3/2nRT. The internal energy is proportional to the temperature so that doubling the temperature results in a doubling of the internal energy: Tf/Ti= Uf/Ui = 2.
Four solid, uniform objects are placed in a container of water (see the figure below). Rank their densities from highest to lowest.
The correct choice is: D > A > C > B. Object D must have the highest density because it is the only object that doesn't float so that ρD > ρfluid. For a floating object, the submerged fraction is proportional to its density so the proper ranking from highest to lowest density is D, A, C, B. For a floating object, the submerged fraction is Vfluid/Vobj= ρobj/ρfluid, where Vfluid is the volume of the displaced fluid (equal to the submerged volume) and Vobj is the object's total volume. As the object's density increases, the displaced volume increases and the object floats lower in the fluid.
An ideal gas undergoes an adiabatic process so that no energy enters or leaves the gas by heat. Which one of the following statements is true? The temperature increases if the gas pressure increases, the temperature decreases if the gas pressure increases, because no energy is added by heat the temperature cannot change, the temperature decreases if the gas volume decreases, the temperature increases if the gas volume increases.
The temperature increases if the gas pressure increases. In an adiabatic process, Q = 0 so that ΔU = W.
internal energy
U--- Increase in U means an increase in temperatue
Density
Usually the density of a solid is more than a liquid, but in the case of ice, the solid (ice) is less in density than the water
In which of the following cases would the maximum "contact pressure" from the floor on a person be the least? when the person is lying down on the floor when the person is sitting on the floor when the person is standing on the floor when the person is standing tiptoes on the floor
When the person is lying down on the floor. P=F/A. Larger area, less force
An ice cube wrapped in a wool blanket remain frozen for
a longer time than an identical ice cube exposed to air at room temperature.
radiation
all things radiate (emit light) according to temperature
first law of thermodynamics
always flows from hot to cold
One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea level everywhere in the world. Where is this problem the most worrisome? at the north pole, where most of the ice floats on water at the south pole, where most of the ice sits on land both at the north and south poles equally at neither pole
at the south pole, where most of the ice sits on land
thermometers
based on principle that some physical property of a system changes as the systems temperature changes
calorimetry problems
conservation of energy, two types of heat: 1) associated with a temperature change 2) associated with a phase change heat gained + heat lost= 0 Q=mL (In calorimetry problems, we need +/- sign)--- "-" when gas to liquid or liquid to solid, "+" when liquid to gas or solid to liquid (Assuming we have a closed system, not losing heat to surroundings)
First law of thermodynamics
conservation of energy. Heat added to a system can either increase the internal energy of the system or do work
venus
could fly on venus thick atmosphere rains acid (95% carbon dioxide)
change in internal energy
delta U= nCvdeltaT
planetary atmosphere
designing materials with specific properties--- understand how particles that make up something imply different properties
The density of lead is greater than iron, and both metals are denser than water. Is the buoyant force on a solid lead object greater than, equal to, or less than the buoyant force acting on a solid iron object of the same dimensions? greater than, equal to, less than
equal to
work done by gas on environment
expanding + work compressing (contracting) - work
work done on gas
expanding - work compressing (contracting) + work *must change signs if work done on gas
Two objects with different sizes, masses, and temperatures are placed in thermal contact. Choose the best answer. Energy travels from the larger object to the smaller object from the object with more mass to the one with less mass from the object at higher temperature to the object at lower temperature
from the object at higher temperature to the object at lower temperature (Only thing that matters is that temperature flows from hot to cold)
beattle juice
giant and very bright red star (500 light years away)
Jupiter
has hydrogen and helium (makeup like the sun)
energy in thermal processes
heat Q vs internal energy U
convection
heat rises and cools off, then goes back down
Earth
helium escapes, Earth cant hang onto it
zeroth law of thermodynamics
if objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other
Two pipes are smoothly connected together without leaks. One has a diameter of 3 cm, and the other has a diameter of 5 cm. Water flows through the pipes. In which pipe is the volume flow the greatest? in the pipe that the water flows through the first (upstream) pipe in the 3 cm pipe in the 5 cm pipe in neither, the flow rate is the same in both pipes
in neither, the flow rate is the same in both pipes
(b) Rank them from least to greatest amount of energy transferred by heat if enough energy is transferred so that each increases in temperature by 20°C.
iron<glass<water
Conservation of angular momentum
is skater pulling arms in to rotate around faster. Li=Lf
types of thermal processes
isobaric, iso-volumetric, isothermal, adiabatic
A metallic ring of 1 cm diameter is placed in a fire and heated up. What would you expect would happen to the inside diameter of the ring as it heats up? it will shrink as the metallic portion expands it will expand as the metallic portion expands It will stay the same size as the metallic portion expands it is impossible to say what will happen to the open area in the center of the ring
it will expand as the metallic portion expands
L
latent heat (depends on material and phase)
Lf
latent heat of fusion
Lv
latent heat of vaporization
PV diagrams
less work done when the majority of the work is being done at a lower pressure
thermal expansion
must take thermal expansion into account when designing anything outdoors or even indoors. Challenger space shuttle is an example of thermal expansion--- space shuttle blew up being launched from Florida (freezing at the time)
adiabatic
no heat is exchanged with surroundings Q=) delta U= W
"Black body"
perfect emitter and perfect absorber (Ex: star)
what happens to the pressure of blood in an artery when plaque starts ti build up on the artery sides?
pressure must decrease because faster velocity
isobaric
pressure stays constant, horizontal line on PV diagram
specific heat C
resistance to change in temperature. directly proportional to Q Q=cmdeltaT being surrounded by water makes weather consistent because of high specific heat of water
Planets
rotation has kinetic energy associated with it, rocky inner planets and gasy outer planets
thermal equilibrium
same temperature--- average KE
States of matter
solid, liquid, gas, plasma --- 5% dark matter--- 25% Energy (Dark)--- 70% Must add energy (heat) to change from one state of matter to the next, plasma=electrons separated from their nuclei (ionization)
isothermal
temperature stays the same constant temp--- no delta U
thermal physics
temperature, thermal equilibrium, thermal contact, heat
P=Q/delta T
the bigger the temp difference, the bigger the power output
Pressure
the force exerted by a fluid on a submerged object at any point is perpendicular to the surface of the object. P= mg/A. P= force/area
molar specific heat
the molar specific heat at constant volume for ideal gas--- CV= 3/2 R U--- KE particles (types of KE: rotational, translational, vibrational)
the greenhouse effect
the solar energy is the energy source for all atmosphere, in greenhouse effect, some energy is trapped by infrared absorbing gases in the atmosphere, raising Earth's temperature
what happens to the speed of blood in an artery when plaque starts to build up on the artery's sides?
the speed of the blood increases in an artery when the plaque is building up because area decreases
the solar atmosphere
the sun- photosphere (coolest spot), chromosphere, corona (spikes to 1 mil Kelvin, solar wind expands out to solar system) sun has strong magnetic field around eruptions pump energy into solar winds---creates high temperature a lot of energy per particle
Two spheres are made of the same metal and have the same radius, but one is hollow and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more? they expand by the same amount, not enough information to say solid sphere, hollow sphere
they expand by the same amount
markings to indicate length are placed on a steel tape in a room that is at a temperature of 22 degrees C. Measurements of a plot of land are then made with the same tape on a day when the temperature is 30 degrees C. Are the measurements too long, too short, or too accurate
too short
Equation of continuity
volume flow rate is constant. Faster in smaller part of the tube, slower in bigger part
properties include
volume of a liquid, dimensions of a solid, pressure of gas at a constant volume, volume of a gas at a constant pressure, the electric resistance of a conductor, the color of an object- red hot metal for example (light that is emitted, not reflected) *be careful because an object can have both emitted and reflected light
At 0 degrees C water freezes and at 4 degrees C water is a liquid
water is most dense at 4 degrees C--- at bottom of Lake Tahoe, water is likely 4 degrees C
Suppose you have 1 kg each of iron, glass, and water, and all three samples are at 10°C. (a) Rank the samples from lowest to highest temperature after 100 J of energy is added to each by heat.
water<glass<iron
phase change
when a substance changes from one form to another during a phase change, there is no change in temperature Q=mcdelta T Q=mL
Bernoulli's Principle
when the speed of a fluid increases, internal pressure in the fluid decreases. From conservation of energy, KE1+PE1+W1=KE2+PE2+W2
