Chapter 7 Thermodynamics

During process D→A, the gas is placed in an insulated container, so that no heat can pass in or out. What is the name for this process? A. Isochoric B. Isothermal C. Adiabatic D. Isobaric

C

Example of a closed system

Gasses in vessels

For a perfectly insulated system, what are the values of Delta E and Q if W = +100 J? A. Delta E = -100J and Q = 0 B. Delta E = 0 and Q = -100J C. Delta E = +100J and Q = 0 D. Delta E = 0 and Q = +100J

A

During an adiabatic compression of a gas the temperature: A. Increases because no heat is transferred B. Remains constant because heat is transferred C. Remains constant because no heat is transferred D. Decreases because heat is transferred

A; During an adiabatic process, no heat is exchanged between the system and its surroundings (Q = 0), this eliminates choices B and D. For an adiabatic process, the change in internal energy of the system is equivalent to the negative work done by or positive work done on the system. When a gas is compressed, work is done on the gas. The temperature of the gas increases as a result.

An expanding gas in an adiabatic piston cylinder system: A. cools because its internal energy is decreasing. B. cools because heat is decreasing. C. warms because internal energy is increasing. D. warms because heat is increasing.

A; Adiabatic means that the boundary is insulated, and no heat transfer can occur. Thus, the heat term in the first law goes to zero, and choices B and D can be eliminated. As the gas expands, it does work on the surroundings, which results in a negative work term. This means that internal energy has to decrease, causing the gas to cool (choice A is correct).

Which of the following true about the process A→B, assuming that the temperature is constant? I. No heat is exchanged between the gas and the environment. II. No work is done by the gas. III. The pressure of the gas decreases. A. III only B. I only C. I and III only D. I, II, and III

A; Assuming the temperature is constant, in process A→B the pressure of the gas decreases. The temperature is constant, so the process A B is an isothermal expansion. In order for the gas to expand without changing temperature, heat must be put into it while the gas does positive work on the environment equal to the area under the curve. (Recall that for an isothermal process, the first law of thermodynamics yields Q = W.) Thus statements I and II and false. Statement III is true because point B is lower than point A on the P axis, so pressure has decreased.

Heat is added to gas in a piston-cylinder, causing the piston to rise. Which of the following terms describes this process? A. Isobaric B. Isochoric C. Isothermal D. Adiabatic

A; Because volume is changing, this process cannot be isochoric (eliminating choice B). Heat is crossing into the system, so it cannot be adiabatic either (eliminating choice D). As heat is added, the temperature of the gas will increase (eliminating choice C), causing the gas particles to move faster. These particles push with more force on the piston, causing it to rise, expanding the volume, and thereby maintaining the pressure of the gas inside equal to the pressure on the piston. This makes the process isobaric since the pressure remains constant over the course of the process.

Suppose you want to raise the temperature of an ideal gas while assign the lowest possible amount of heat and doing no work on the gas. Which process should you use? A. Isobaric B. Isochoric C. Isothermal D. Adiabatic

B

During process B→C (isochoric), what is true about the change in temperature of the gas? A. The temperature decreases as heat transfers out of the gas. B. The temperature decreases as work is done by the gas. C. The temperature increases as work is done on the gas. D. The temperature increases as heat transfers into the gas.

A; During process B→C, the temperature decreases as heat transfers out of the gas. Because there is no change in volume between states B and C—an isochoric process—no work is done by or on the gas. This eliminates the choices involving work. Between states B and C, the pressure of the gas decreases. By the ideal gas law, if pressure decreases as volume is kept constant, temperature must decrease as well (P ∝ T). In order for temperature to decrease while no work is being done, heat must pass out of the system: ΔE = Q - W = Q, so ΔE < 0 implies Q < 0.

What is an adiabatic process?

An adiabatic process is where no thermal energy is transferred between the system and its surroundings. (Q = 0)

A rod composed of some unknown material with an initial length of 2 m is heated by 40 °C and is found to have increased in length by .4 mm. What is its coefficient of linear thermal expansion, α? A. 5 × 10-2 K-1 B. 5 × 10-6 K-1 C. 5 × 10-5 K-1 D. 5 × 10-3 K-1

B; ΔL = aLΔT 4 x 10^-4 = (a)(2)(40) 4 x 10^-4 = 80a 400 x 10^-6 = 80a 5 x 10^-6 = a

Which of the following terms describes a vertical line on a P-V diagram? A. Isobaric B. Isochoric C. Adiabatic D. Isothermal

B; A P-V diagram plots variations in pressure and volume of a system while keeping all other variables constant. A vertical line would indicate one of these variables changes while the other remains constant. Isothermal means constant temperature (eliminating choice C), while adiabatic means no heat exchange between system and surroundings (eliminating choice D). You should expect volume to be on the horizontal axis of the graph, indicating a constant volume, or isochoric system (choice B). Isobaric means constant pressure and would be a horizontal line (eliminating choice A).

A gas undergoes isothermal expansion. Given that the gas does positive work on the environment, which of the following accurately describes the heat input to the system, Q, and the change in internal energy, ΔE? A. Q > 0, ΔE > 0 B. Q > 0, ΔE = 0 C. Q < 0, ΔE = 0 D. Q = 0, ΔE > 0

B; A gas undergoes isothermal expansion. Given that the gas does positive work on the environment, Q > 0 and ΔE = 0. An isothermal process by definition occurs at a constant temperature, so ΔE = 0. Because the gas is doing positive work on the environment, heat must be passing into the system by the first law of thermodynamics: ΔE = Q - W = 0, so Q = W > 0.

The linear thermal expansion of a metal rod is given by ΔL = aL0ΔT. By how many degrees Celsius would the temperature of a rod have to increase for the rod's length to increase by 20%? A. aL0/5 B. 1/5a C. It depends on the original length of the rod D. Cannot be determined because Kelvins must be used for ΔT

B; An increase of 20% is the same as saying ΔL/L0 = .2, so L is not needed in the equation eliminating A and C. The answer is B.

Imagine the following scenario: a metallic cube of temperature T1, sitting on a horizontal surface, is being heated with a heat gun aimed vertically down on its top surface. After some time has passed, the temperature of the cube is measured to be higher: T2 > T1. The heat gun is removed. Then, with no external force applied, the cube suddenly accelerates along the surface. After traveling some distance d, it slows and stops, and its temperature is measured again and is shown to have decreased to T3, such that T1 < T3 < T2. What physical law is definitely violated in this scenario? A. Conservation of mechanical energy B. The second law of thermodynamics C. Conservation of total energy D. The first law of thermodynamics

B; The second law of thermodynamics states that energy will not spontaneously transform from a less ordered state (like thermal energy of a warm block) to a more ordered state (like the macroscopic kinetic energy of a sliding block). It is therefore violated by the scenario described in the question. Because the block is sliding to a stop on a horizontal surface that presumably has some kinetic friction coefficient with the block, conservation of mechanical energy is not violated. Conservation of total energy essentially is the first law of thermodynamics, so neither of those answer choices can be correct. Indeed, neither is violated because the internal energy (measured as T2) of the block after it has been heated by the environment (the heat gun) is greater than its internal energy (measured as T3) after it has displaced some distance along the surface, indicating that some thermal energy has transformed into kinetic energy and the total energy may well be constant.

This closed curve describes the working of a reversible heat engine, which takes heat QH from a high temperature (TH in kelvins) source and expels heat (QL) into a cold temperature (TC in kelvins) heat sink, simultaneously doing work on its environment. The second law of thermodynamics can be formulated to say that the efficiency of converting heat to work of a heat engine is given by e = 1 - QL / QH = 1 - TC / TH. All of the following measures could be used to improve the efficiency of a heat engine except: A. to vent heat into a cold river flowing out of the snow-covered hills instead of into a small lake that heats up over time. B. to cool the engine with a negative temperature heat sink, thus increasing its efficiency to a value greater than 1. C. to build with materials that conduct heat more effectively for those processes that take place in contact with the high-temperature and low-temperature source and sink. D. to use a hotter burning fuel as the heat source.

B; This closed curve describes the working of a reversible heat engine, which takes heat QH from a high temperature (TH in kelvins) source and expels heat (QL) into a cold temperature (TC in kelvins) heat sink, simultaneously doing work on its environment. The second law of thermodynamics can be formulated to say that the efficiency of converting heat to work of a heat engine is given by e = 1 - QH / QL = 1 - TC / TH. Cooling the engine with a negative temperature heat sink, thus increasing its efficiency to a value greater than 1 could not be used to increase efficiency. The lowest possible temperature by definition is 0 K, so it is not possible for the engine to transfer heat to a negative temperature source. All the other situations described are realistic ways of increasing efficiency.

During process C → D (isobaric), how much work is done by the gas on the environment? Assume the pressure is equal to P0 and the volumes are VC and VD, respectively. A. 0 J B. P0(VC - VD) C. P0(VD - VC) D. Cannot be determined from the information given.

C

Question: Compare a huge glacier to a red hot piece of coal. Which of the following is true? A. The charcoal contains more thermal energy and has a higher temperature than the glacier. B. The charcoal contains more thermal energy and has a lower temperature than the glacier C. The charcoal contains less thermal energy and has a higher temperature than the glacier D. The charcoal contains less thermal energy and has a lower temperature than the glacier

C

Which of the following is the most plausible thermodynamic description of the Earth's climate patterns? A. The Earth absorbs heat from the Sun via convection from the solar wind. This heat passes over the entire earth as the current of the solar wind envelops the planet, which explains the relative consistency of temperatures across the globe. B. The Earth absorbs heat from the sun via conduction, as solar photons cause the particles they hit on the Earth to vibrate more rapidly. This heat moves around the world as convection in the atmosphere. C. The Earth absorbs heat from the Sun via radiation. This heat partly drives convection currents in the air and water which move heat around the globe, keeping the whole Earth a much more consistent temperature than it would be if there were no atmosphere. D. The Earth absorbs heat from the Sun via radiation. This heat moves around the globe via conduction, explaining why air at ground level is always warmer than higher in the atmosphere.

C

An expanding spring pushes a rigid cylinder of gas across a horizontal frictionless table. Consider the system to be the gas inside the cylinder. Which of the following sets of relations best describes what happens? A. W(on system) > 0, Q > 0, ΔKE > 0 B. W(on system) > =, Q = 0, ΔKE = 0 C. W(on system) > 0, Q = 0, ΔKE > 0 D. W(on system) > 0, Q < 0, ΔKE > 0

C; An expanding spring exerts a force that causes a mass to displace, so it does (+) work, eliminating B Because work is (+) and the gas is neither expanding or compressing, it is translated to KE, so KE is (+). There is no friction and no mention of a temperature differential that would move heat into or out of the system, so Q = 0

Three blocks of equal mass are composed of different metals. Each begins at a different temperature. The three are placed into contact with one another in order block 1, block 2, and block 3. If they are allowed to reach thermal equilibrium, all of the following are possible outcomes except: A. Blocks 2 and 3 both partially melt while block 1 remains completely solid. B. Block 1 absorbs more heat from block 2 than block 3 transfers into block 2.Your Answer C. Block 1 is a lower temperature than block 2, which in turn is a lower temperature than block 3. D. Block 1 melts completely while blocks 2 and 3 remain solid.

C; Note that this is an except question, asking for the statement that is false. The zeroth law of thermodynamics states that when objects reach thermal equilibrium, all will be the same temperature. This makes the statement "Block 1 is a lower temperature than block 2, which in turn is a lower temperature than block 3" false, and thus the correct answer. Each of the other choices is possible. Because different metals have different melting points, one block of metal with a high melting point could begin at a higher temperature than the melting point of another block, and as the first block transfers heat into the second block (which it would have to do because heat always flows from higher temperature to lower temperature), the temperature of the second block could rise sufficiently to reach its melting point, with additional heat melting the second block partially or completely. Thus the choices describing the partial or complete melting of one or two blocks are true statements and can be eliminated. The zeroth law places a constraint on temperature and the direction of heat flow, but not on the amount of heat flow. Conservation of energy—the first law of thermodynamics—dictates that the flow in a system in which no work is done be equal to the change in energy. This is consistent with the choice "Block 1 absorbs more heat from block 2 than block 3 transfers into block 2" so long as the differences between the temperatures of block 1 and block 2 between block 2 and block 3 be different, or the metals have different heat capacities. Thus that statement is true and the choice can be eliminated.

A closed system consisting of a ballon expands by 5 x 10^-2 L at constant temperature in an environment with a pressure of 1.0 x 10^5 Pa. What is the value of heat transfer in this process?

Convert L to m^3 --> 5 x 10^-2 L = 5 x 10^-5 m^3 W = PΔV W = (1.0 x 10^5 Pa)(5 x 10^-5 m^3) W = 5J At constant temperature, ΔE = 0 First law reduced to 0 = Q - W, Q = W --> 5J

An amount of heat Q is added to a system. Which of the following can result? I. its temperature increases II. its phase changes III. it undergoes isothermal expansion a. I only b. I or II only c. I or III only d. I, II, or III

D

An ideal gas is held under pressure in an isolated container behind a thin membrane opposite which is a vacuum, like an inflated ballon in a large evacuated room. The membrane is suddenly ruptured, like popping the balloon. What happens next? A. Nothing: the membrane ruptures but the gas is unaffected. B. The pressure and temperature both decrease rapidly. C. The temperature decreases rapidly but the pressure stays constant D. The pressure decreases rapidly, but the temperature remains constant

D

Which of the following are true about heat and temperature? A. Heat flows from a higher temperature material to a lower temperature material and in the process always raises the temperature of the second material. B. Both heat and temperature can be measured in kelvins. C. A hotter object always contains more thermal energy than does a cooler object. D. The temperature of a material is directly proportional to the kinetic energy of its constituent particles.

D

The rate of heat conduction across a piece of material of length L and cross-sectional area A is given by , where Ti and Tf are the temperatures on either side of the material, and k is the thermal conductivity of the material. A woman hiking in the mountains wears a winter coat filled with goose down (thermal conductivity of 0.025 W/m∙K), and in the process produces 7.2 × 105 J of body heat per hour. If her body's surface area is roughly 1.5 m2, how thick must her coat be to maintain body temperature if the air temperature is -3 °C? Equation to use: delta Q/delta T = (kA (Ti - Tf) L A. 1.2 cm B. 0.12 mm C. 2 μm D. 7.5 mm

D;

The rate of heat conduction across a piece of material of length L and cross-sectional area A is given by delta Q/delta t, where Ti and Tf are the temperatures on either side of the material, and k is the thermal conductivity of the material. What are the units of heat conduction rate? A. kelvin - meters B. kelvins per second C. joules per kelvin D. watts

D;

An ice cube is dropped into a thermos half full with cool water. The thermos is then immediately resealed. Assuming the ice cube partially melts, which of the following best describes the change in state of the system after the thermos has been resealed? A. Q = 0, ΔE < 0, entropy stays the same B. Q < 0, ΔE = 0, entropy increases C. Q < 0, ΔE < 0, entropy stays the same D. Q = 0, ΔE < 0, entropy increases

D; A closed thermos is an insulated system that doesn't allow heat to pass in or out, so Q = 0. If the ice partially melts, the initial temperature of the water must have been slightly greater than freezing (so that heat would pass from the water into the ice and melt it). Therefore the temperature must have decreased, and ΔE < 0. Because the liquid phase of a substance is more disordered (has greater entropy) than the solid phase, the entropy of the system increases as the ice melts.

Heat transfer is most likely to occur: A. due to the expansion of a gas in an insulated system. B. due to the compression of a gas in an insulated system. C. due to the contact of two substances with the same internal energies. D. due to the contact of two substances of differing initial temperature.

D; According to the zeroth law of thermodynamics, heat transfer occurs when two objects of differing temperature come into contact (choice D is correct). Given that temperature is a measure of internal energy, we would expect no heat exchange when two objects have the same internal energies (choice C is wrong). Work is commonly discussed in terms of expansion and compression of gases but heat transfer will not occur in an insulated system (choices A and B are wrong).

This closed curve describes the working of a reversible heat engine, which takes heat from a high temperature source and expels heat into a cold temperature heat sink, simultaneously doing work on its environment. Which of the following phenomena best fits this description? A. Water flowing down a river passes over a waterwheel, turning it and doing work in the process. The water then returns to a lower part of the river and continues flowing downhill. B. A gasoline-air mixture is injected into a piston through an intake valve, is rapidly compressed, and then is ignited by a spark. The rapid pressure increase at constant volume then forces the piston up, after which an exhaust valve is opened to allow the spend fuel mixture to pass out of the piston and exit the engine. C. Water in a teapot is set on the stove to boil, building up pressure until the steam pushes through a valve on the spout. The steam rapidly cools and condenses in the air, returning back to a liquid state that falls as droplets on the kitchen floor. D. Burning coal heats and expands water vapor, which pushes through pipes to turn a turbine. The steam then enters a sealed chamber immersed in cold water and is allowed to cool for a few minutes before being slowly compressed while still cooling. The chamber is then removed from the cold-water bath, and the gas is further compressed before being released through a valve back into the coal-heating region.

D; Burning coal heats and expands water vapor, which pushes through pipes to turn a turbine. The steam then enters a sealed chamber immersed in cold water and is allowed to cool for a few minutes before being slowly compressed while still cooling. The chamber is then removed from the cold-water bath, and the gas is further compressed before being released through a valve back into the coal-heating region best fits this description. The waterwheel example describes purely mechanical work, not a thermodynamic process, so it can be rejected. The teapot example is clearly not a closed system, because the steam that leaves the teapot does not return to it. Moreover, it is unclear that the teapot's set of processes does any work, eliminating that choice. The gasoline four-stroke engine described is also not technically a closed system, because the spent fuel enters the environment, but such systems are sometimes modeled as idealized closed systems. Another problem, however, is that the cycle described clearly does not fit the given P-V graph: for one thing, it describes a "rapid pressure increase at constant volume." That would have to be an isochore with the arrow pointing up, but no such process appears on the given graph, eliminating that answer choice. The coal-fired turbine system described fits the processes in the graph.

During process D→A, the gas is compressed while in an insulated container, so no heat can pass in or out of the system. Let TD and TA be the temperatures as states D and A, respectively. Which of the following is true? A. TD > TA B. The relationship between TD and TA cannot be uniquely determined. C. TD = TA D. TD < TA

D; During process D→A, the gas is compressed while in an insulated container, so no heat can pass in or out of the system. Let TD and TA be the temperatures as states D and A, respectively. TD < TA is true. Because the process D A involves no heat transfer, the first law of thermodynamics yields ΔE = Q - W = -W. As the gas is compressed between states D and A, negative work is done by the system, so W < 0. Therefore ΔE > 0. If the internal energy of a gas increases, so does its temperature.

This closed curve describes the working of a reversible heat engine, which takes heat QH from a high temperature (TH in kelvins) source and expels heat (QL) into a cold temperature (TC in kelvins) heat sink, simultaneously doing work on its environment. The efficiency of such a heat engine is given by the relation e = W / QH. Which of the following is also an expression for efficiency? A. W / TC - TH B. (QL - QH) / QH C. W / TH - TC D. (QH - QL) / QH

D; This closed curve describes the working of a reversible heat engine, which takes heat QH from a high temperature (TH in kelvins) source and expels heat (QL) into a cold temperature (TC in kelvins) heat sink, simultaneously doing work on its environment. The efficiency of such a heat engine is given by the relation e = W / QH. (QH - QL) / QH is also an expression for efficiency. The answer must be unitless as is the expression given in the question, so the choices with work / temperature (units of J/K) can be eliminated. QL - QH is negative, and a negative efficiency intuitively should not make sense, eliminating that choice. Solving for the correct expression requires the fact that a closed set of reversible processes like this returns to the same state every cycle, meaning the change in internal energy of the system from A→B→C→D→A is zero. Thus the first law of thermodynamics yields 0 = Q - W, so W = Q = QH - QL.

What is the first law of thermodynamics?

Energy can be transferred and transformed, but it cannot be created or destroyed.

Fahrenheit to Celsius conversion

F = 9/5C + 32

KE of temperature equation

KE = 1/2mv^2 = 3/2 KB T KE = kinetic energy (J) m = mass (kg) v = velocity (m/s) KB = Boltzmann constant (1.38 x 10^-23 J/K) T = temperature

What are intrinsic properties?

Physical properties that are not dependent on how much of the substance is present.

What are extrinsic properties?

Physical properties that change depending on the amount of the substance present.

What is a system?

Portion of the universe that we are interested in observing

Heat gained or lost (phase change)

Q = mL

What is temperature?

The measure of the average kinetic energy of the molecules.

What is convection?

The transfer of heat by the movement of a fluid

Assume that point A corresponds to a pressure of 500 kPa and a volume of 0.5 m3 and that point B corresponds to a pressure of 300 kPa and a volume of 2 m3. The pressure at points C and D is 100 kPa. Approximately how much work is done by the gas during process A → B? A. 4.5 × 10^5 J B. 4.5 × 10^2 J C. 6 × 10^5 J D. 6 × 10^2 J

The work done by a thermodynamic process is equal to the area under its curve on the P-V graph (positive if the curve progresses positively in V, negative if it progresses negatively). In this case, the area under the A B curve can be approximated as the sum of a rectangle with base 2 - 0.5 = 1.5 m3 and height 300 kPa and a triangle with a base of 1.5 m3 and a height of 500 - 300 = 200 kPa. This yields W = (1.5)(3 × 105) + ½(1.5)(2 × 105) = 6 × 105 J. Note that the pressure at states C and D is irrelevant to the work done between states A and B.

What does an isochoric PV diagram look like?

Vertical line

What does the first law equation yield in an isochoric process?

W = 0, so first law yields ΔU = Q

Work equation (with pressure and volume)

W = PΔV

What does the first law yield in an isothermal process?

W = Q

What are isolated systems?

no exchange of mass or energy is possible

What is an isothermal process?

a process that occurs at constant temperature (delta E = 0)W

What is the third law of thermodynamics?

absolute zero cannot be reached

What are open systems?

allow the exchange of mass and energy with the surroundings

What is an isobaric process?

an isobaric process is a process that takes place at constant pressure

example of an isolated system

bomb calorimeter

When work is positive, work is being done ______ the system

by

Examples of convection

candles and convectional ovens

What are closed systems

capable of exchanging energy but not mass

What is an isochoric process?

constant volume

What are process functions?

describe the path taken to get from one state to another Heat and work are the two examples

Radiation is the transfer of energy by __________ waves

electromagnetic

What are the surroundings?

everything outside the system

When Q > 0, heat transfers _______ the system

into

Coffee cup calorimeters attempt to create _______ systems

isolated

What is entropy?

measure of disorder

Work is the transfer of _________ energy

mechanical

What is the zeroth law of thermodynamics?

objects are in thermal equilibrium only when their temperatures are equal

When work is negative, work is being done ________ the system

on

Example of an open system

organisms, pot of water on the stove

When Q < 0, heat transfers ______ of the system

out

In conduction, there must be _______ contact

physical

Heat gained or lost (with temperature change)

q = mcΔT

What does a PV diagram of an isobaric process look like?

rectangle

What are state functions?

state functions are pathway independent and describe the current state of a system. If you know 3 state functions (one of which must be extrinsic), then you can extrapolate all the other state functions for that material/ state 1. internal energy (U) 2. temperature (T) 3. pressure (P) 4. volume (V) 5. enthalpy (H) 6. entropy (S) 7. gibbs energy (G)

What is heat?

the transfer of thermal energy

What is conduction?

transfer of energy from one place to another by contact

What does the first law yield in an adiabatic process?

ΔE = -W

Thermal expansion equation

ΔL=αLΔT ΔL = change in length (m) α = coefficient of linear expansion (K^-1 or C^-1) L = length (m) ΔT = change in temperature

change in entropy equation

ΔS = Qrev/T S is entropy in J/molK Qrev is the heat gained/lost in a REVERSIBLE PROCESS T is temp in Kelvin

Second law of thermodynamics equation

ΔS(universe) = ΔS(systm) + ΔS(surround) > 0

What is the first law equation in an isobaric process?

ΔU = Q - PΔV

First law of thermodynamics equation

ΔU = Q - W ΔU = change in internal energy Q = heat W = work

Volumetric expansion equation

ΔV=BVΔT ΔV = change in volume (m^3) B = V = volume (m^3) ΔT = change in temperature