Question 1

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not.
-(d) The sun

Accepted Answer

A) True 
 B)False

Question 2

Consider a system consisting of two Einstein solids $P$ and $Q$ in thermal contact. Assume that we know the number of atoms in each solid and $\varepsilon$. What do we know about the system if we also know the total energy in each of the two objects?

Accepted Answer

A)  Its macrostate 
B)  Its microstate 
C)  Its macropartition 
D)  Its microstate and macropartition 
E)  Its macrostate and macropartition
F) Its macrostate and microstate
G) Its macrostate, microstate, and macropartition 
A)  Its macrostate 
B)  Its microstate 
C)  Its macropartition 
D)  Its microstate and macropartition 
E)  Its macrostate and macropartition
F) Its macrostate and microstate
G) Its macrostate, microstate, and macropartition

Question 3

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process:
  
-What are the signs of $Q, W$, and $\Delta U$ for the process $C \rightarrow A$ ?

Accepted Answer

A)  $0,-,-$ 
B)  $\mathbf{0},+,+$ 
C) ,,+- 0 
D) ,,++ 0 
E) ,,-+ 0
F) Other (specify) 
A)  $0,-,-$ 
B)  $\mathbf{0},+,+$ 
C) ,,+- 0 
D) ,,++ 0 
E) ,,-+ 0
F) Other (specify)

Question 4

In the situation shown in figure T2.5c, the width of the bell curve at half its peak value is $0.021 U$. If we multiply $N_{A}$, $N_{B}$, and $U$ by a factor of 100 , then the peak's width (as you can check) is about $0.0021 U$. Suppose that we increase each solid's $N$ and the system's total energy by another factor of $10^{18}$ to create solids containing $1 / 6$ of a mole of atoms (still pretty small objects by everyday standards). Assuming that the trend continues, what will be the approximate width of the combined system's probability bell curve as a fraction of $U$ ?

Accepted Answer

A)  $2 \times 10^{-20}$
(c) 0.0 
B)  $2 \times 10^{-22}$
Figure T2.5 
C)  $2 \times 10^{-10}$ 
D)  $\mathbf{2} \times \mathbf{1 0}^{-12}$ 
E)  $2 \times 10^{-40}$
F) $2 \times 10^{-42}$
$\mathrm{T}$. Some other factor (specify). 
A)  $2 \times 10^{-20}$
(c) 0.0 
B)  $2 \times 10^{-22}$
Figure T2.5 
C)  $2 \times 10^{-10}$ 
D)  $\mathbf{2} \times \mathbf{1 0}^{-12}$ 
E)  $2 \times 10^{-40}$
F) $2 \times 10^{-42}$
$\mathrm{T}$. Some other factor (specify).

Question 5

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!)
-(b) A ball is dropped and falls freely downward.

Accepted Answer

The answer of Characterize each of the following processes as...

Question 6

Consider each of the following processes. Is the process consistent (C) or inconsistent (D) with the limitations on equation T8.12 $d S=\frac{d Q}{T}$ (that $N$ be fixed and that the process not involve any energy transfer that is neither heat nor work due to a quasistatic volume change)?
-b) A closed vial of gas is heated with a flame.

Accepted Answer

A)  Consistent 
B)  Inconsistent 
A)  Consistent 
B)  Inconsistent

Question 7

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process:
  
-What are the signs of $Q, W$, and $\Delta U$ for the process $A \rightarrow B$ ?

Accepted Answer

A)  $0,-,-$ 
B)  $0,+,+$ 
C) ,,+- 0 
D) ,,++ 0 
E) ,,-+ 0
F) Other (specify) 
A)  $0,-,-$ 
B)  $0,+,+$ 
C) ,,+- 0 
D) ,,++ 0 
E) ,,-+ 0
F) Other (specify)

Question 8

Suppose that we allow an ideal gas containing $N$ atoms to expand slowly and isothermally to twice its initial volume. By what factor does its multiplicity increase?

Accepted Answer

A)  By a factor of 2 . 
B)  By a factor of $2^{N}$. 
C)  The multiplicity does not change. 
D)  The answer depends on the gas's initial volume. 
E)  The answer depends on the gas's fixed temperature. 
A)  By a factor of 2 . 
B)  By a factor of $2^{N}$. 
C)  The multiplicity does not change. 
D)  The answer depends on the gas's initial volume. 
E)  The answer depends on the gas's fixed temperature.

Question 9

$N$ molecules of a monatomic gas $A$ are mixed with the same number of molecules of a diatomic gas $B$ in a container, and the mixture is held at a constant temperature $T$ (which is about equal to room temperature). The molecules of gas $A$ have mass $m_{A}$, and the molecules of gas $B$ have mass $m_{B}>m_{A}$ Which gas has In each case, choose from one of the four answers below.
-(c) the greater total thermal energy $U$, and

Accepted Answer

A)  The quantity is greater for gas $A$. 
B)  The quantity is greater for gas $B$. 
C)  The quantity is the same for both gases. 
D)  One does not know enough to compare the quantities. 
A)  The quantity is greater for gas $A$. 
B)  The quantity is greater for gas $B$. 
C)  The quantity is the same for both gases. 
D)  One does not know enough to compare the quantities.

Question 10

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not.
-(b) An automobile engine

Accepted Answer

A) True 
 B)False

Question 11

The earth's equilibrium temperature depends on its radius.

Accepted Answer

A) True 
 B)False

Question 12

Suppose that a bubble of helium (a monatomic gas) rising from the bottom of the ocean expands in volume by a factor of 8 by the time it reaches the surface [where the pressure is 1 atmosphere (atm)]. Assume that the bubble rises so fast that it expands essentially adiabatically. What was the pressure on the gas at the depth where it formed (in atmospheres)?

Accepted Answer

A)  $3.5 \mathrm{~atm}$ 
B)  $8 \mathrm{~atm}$ 
C)  $16 \mathrm{~atm}$ 
D)  $18 \mathrm{~atm}$ 
E)  32 atm
F) Other (specify) 
A)  $3.5 \mathrm{~atm}$ 
B)  $8 \mathrm{~atm}$ 
C)  $16 \mathrm{~atm}$ 
D)  $18 \mathrm{~atm}$ 
E)  32 atm
F) Other (specify)

Question 13

We drop a stone of mass $m$ from a height $h$ into a bucket of water. What would be a suitable replacement process for this non-quasistatic process?

Accepted Answer

A)  Lower the stone gently into the water. 
B)  Lower the stone gently into the water, and then heat the water until it has $m g h$ more energy than it had before. 
C)  Lower the stone gently into the water, and then stir the water gently to give it $m g h$ more energy. 
D)  Raise the water up to height $h$, gently put the stone in it, and then lower both back to the ground. 
E)  Either (
B)  or (
C) .
F) None of the above. 
A)  Lower the stone gently into the water. 
B)  Lower the stone gently into the water, and then heat the water until it has $m g h$ more energy than it had before. 
C)  Lower the stone gently into the water, and then stir the water gently to give it $m g h$ more energy. 
D)  Raise the water up to height $h$, gently put the stone in it, and then lower both back to the ground. 
E)  Either (
B)  or (
C) .
F) None of the above.

Question 14

We slowly heat $100 \mathrm{~g}$ of water from 5 to $25^{\circ} \mathrm{C}$. What is its change in entropy? (For water, $c=4186 \mathrm{~kg}$.)

Accepted Answer

A)  $582 \mathrm{~J} / \mathrm{K}$ 
B)  $29.2 \mathrm{~K}$ 
C)  $139 \mathrm{~J} / \mathrm{K}$ 
D)  $6.95 \mathrm{~J} / \mathrm{K}$ 
E)  0
F) Other (specify) 
A)  $582 \mathrm{~J} / \mathrm{K}$ 
B)  $29.2 \mathrm{~K}$ 
C)  $139 \mathrm{~J} / \mathrm{K}$ 
D)  $6.95 \mathrm{~J} / \mathrm{K}$ 
E)  0
F) Other (specify)

Question 15

How does the entropy of $1 \mathrm{~mol}$ of helium gas in a container at room temperature compare to $1 \mathrm{~mol}$ of argon gas in an identical container at the same temperature?

Accepted Answer

A)  The helium gas has greater entropy. 
B)  The argon gas has greater entropy. 
C)  Both gases have the same entropy. 
D)  One needs to know more to answer definitively. 
A)  The helium gas has greater entropy. 
B)  The argon gas has greater entropy. 
C)  Both gases have the same entropy. 
D)  One needs to know more to answer definitively.

Question 16

Which of the speeds $v$ listed below is the lowest speed where the probability of a gas molecule having that speed is negligible compared to that for $v=v_{p}$ ("negligible" meaning less than $1 / 100$ of its value at $v=v_{p}$ ).

Accepted Answer

A)  $v \approx 0.2 v_{p}$ 
B)  $v=2 v_{p}$ 
C)  $v=3 v_{p}$ 
D)  $v=5 v_{p}$ 
A)  $v \approx 0.2 v_{p}$ 
B)  $v=2 v_{p}$ 
C)  $v=3 v_{p}$ 
D)  $v=5 v_{p}$

Question 17

Classify the following hypothetical perpetual motion machines as being perpetual motion machines of the first kind $(A)$ or the second kind (B).
-(c) An engine's tank is filled with water. When the engine operates, it slowly freezes the water in the tank, converting the energy released to mechanical energy.

Accepted Answer

A)  first kind 
B)  second kind 
A)  first kind 
B)  second kind

Question 18

Suppose that you use a super-fast computer to measure a system's macropartition a billion times a second. What is the approximate probability of the least-probable macropartition that you might plausibly see in your lifetime? Select the closest response.

Accepted Answer

A)  1 chance in a million $\left(10^{6}\right)$ 
B)  1 chance in a billion $\left(10^{9}\right)$ 
C)  1 chance in a trillion $\left(10^{12}\right)$ 
D)  1 chance in $10^{15}$ 
E)  1 chance in $10^{18}$
F) 1 chance in $10^{21}$ 
A)  1 chance in a million $\left(10^{6}\right)$ 
B)  1 chance in a billion $\left(10^{9}\right)$ 
C)  1 chance in a trillion $\left(10^{12}\right)$ 
D)  1 chance in $10^{15}$ 
E)  1 chance in $10^{18}$
F) 1 chance in $10^{21}$

Question 19

If we increase a one-dimensional container's length $L$ by a factor of 100 , by what factor does the value of $\varepsilon / k_{B} T$ change at room temperature?

Accepted Answer

A)  10 
B)  100 
C)  10,000 
D)  $1 / 10$ 
E)  $1 / 100$
F) $1 / 10,000$ 
A)  10 
B)  100 
C)  10,000 
D)  $1 / 10$ 
E)  $1 / 100$
F) $1 / 10,000$

Question 20

In each of the processes described below, energy flows across the boundary of the object that serves as the subject of each sentence. Is this energy flow heat (A), work (B), or some other kind of energy transfer (E)?
-(d) Your hands get warm when you rub them together.

Accepted Answer

The answer of In each of the processes described below,...

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not. -(d) The sun

Consider a system consisting of two Einstein solids $P$ and $Q$ in thermal contact. Assume that we know the number of atoms in each solid and $\varepsilon$ . What do we know about the system if we also know the total energy in each of the two objects?

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!) -(b) A ball is dropped and falls freely downward.

Suppose that we allow an ideal gas containing $N$ atoms to expand slowly and isothermally to twice its initial volume. By what factor does its multiplicity increase?

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not. -(b) An automobile engine

The earth's equilibrium temperature depends on its radius.

We drop a stone of mass $m$ from a height $h$ into a bucket of water. What would be a suitable replacement process for this non-quasistatic process?

We slowly heat $100 \mathrm{~g}$ of water from 5 to $25^{\circ} \mathrm{C}$ . What is its change in entropy? (For water, $c=4186 \mathrm{~kg}$ .)

How does the entropy of $1 \mathrm{~mol}$ of helium gas in a container at room temperature compare to $1 \mathrm{~mol}$ of argon gas in an identical container at the same temperature?

Which of the speeds $v$ listed below is the lowest speed where the probability of a gas molecule having that speed is negligible compared to that for $v=v_{p}$ ("negligible" meaning less than $1 / 100$ of its value at $v=v_{p}$ ).

Suppose that you use a super-fast computer to measure a system's macropartition a billion times a second. What is the approximate probability of the least-probable macropartition that you might plausibly see in your lifetime? Select the closest response.

If we increase a one-dimensional container's length $L$ by a factor of 100 , by what factor does the value of $\varepsilon / k_{B} T$ change at room temperature?

In each of the processes described below, energy flows across the boundary of the object that serves as the subject of each sentence. Is this energy flow heat (A), work (B), or some other kind of energy transfer (E)? -(d) Your hands get warm when you rub them together.

Conservation Laws Constrain Interactions

The Laws of Physics Are Universal Newtonian Mechanics

The Laws of Physics Are Frame-Independent Relativity

Electricity and Magnetism Are Unified

Matter Behaves Like Waves Quantum Physics

Filters

Exam 6: Some Processes Are Irreversible Thermal Physics

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not. -(d) The sun

Consider a system consisting of two Einstein solids PPP and QQQ in thermal contact. Assume that we know the number of atoms in each solid and ε\varepsilonε . What do we know about the system if we also know the total energy in each of the two objects?

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process: -What are the signs of Q,WQ, WQ,W , and ΔU\Delta UΔU for the process C→AC \rightarrow AC→A ?

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!) -(b) A ball is dropped and falls freely downward.

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process: -What are the signs of Q,WQ, WQ,W , and ΔU\Delta UΔU for the process A→BA \rightarrow BA→B ?

Suppose that we allow an ideal gas containing NNN atoms to expand slowly and isothermally to twice its initial volume. By what factor does its multiplicity increase?

Which of the following devices are heat engines? In each case, answer T (True) if it is a heat engine, and F (False) if it is not. -(b) An automobile engine

The earth's equilibrium temperature depends on its radius.

We drop a stone of mass mmm from a height hhh into a bucket of water. What would be a suitable replacement process for this non-quasistatic process?

We slowly heat 100 g100 \mathrm{~g}100 g of water from 5 to 25∘C25^{\circ} \mathrm{C}25∘C . What is its change in entropy? (For water, c=4186 kgc=4186 \mathrm{~kg}c=4186 kg .)

How does the entropy of 1 mol1 \mathrm{~mol}1 mol of helium gas in a container at room temperature compare to 1 mol1 \mathrm{~mol}1 mol of argon gas in an identical container at the same temperature?

Which of the speeds vvv listed below is the lowest speed where the probability of a gas molecule having that speed is negligible compared to that for v=vpv=v_{p}v=vp​ ("negligible" meaning less than 1/1001 / 1001/100 of its value at v=vpv=v_{p}v=vp​ ).

Suppose that you use a super-fast computer to measure a system's macropartition a billion times a second. What is the approximate probability of the least-probable macropartition that you might plausibly see in your lifetime? Select the closest response.

If we increase a one-dimensional container's length LLL by a factor of 100 , by what factor does the value of ε/kBT\varepsilon / k_{B} Tε/kB​T change at room temperature?

In each of the processes described below, energy flows across the boundary of the object that serves as the subject of each sentence. Is this energy flow heat (A), work (B), or some other kind of energy transfer (E)? -(d) Your hands get warm when you rub them together.

Conservation Laws Constrain Interactions

The Laws of Physics Are Universal Newtonian Mechanics

The Laws of Physics Are Frame-Independent Relativity

Electricity and Magnetism Are Unified

Matter Behaves Like Waves Quantum Physics

Filters

Consider a system consisting of two Einstein solids $P$ and $Q$ in thermal contact. Assume that we know the number of atoms in each solid and $\varepsilon$ . What do we know about the system if we also know the total energy in each of the two objects?

Suppose that we allow an ideal gas containing $N$ atoms to expand slowly and isothermally to twice its initial volume. By what factor does its multiplicity increase?

We drop a stone of mass $m$ from a height $h$ into a bucket of water. What would be a suitable replacement process for this non-quasistatic process?

We slowly heat $100 \mathrm{~g}$ of water from 5 to $25^{\circ} \mathrm{C}$ . What is its change in entropy? (For water, $c=4186 \mathrm{~kg}$ .)

How does the entropy of $1 \mathrm{~mol}$ of helium gas in a container at room temperature compare to $1 \mathrm{~mol}$ of argon gas in an identical container at the same temperature?

Which of the speeds $v$ listed below is the lowest speed where the probability of a gas molecule having that speed is negligible compared to that for $v=v_{p}$ ("negligible" meaning less than $1 / 100$ of its value at $v=v_{p}$ ).

If we increase a one-dimensional container's length $L$ by a factor of 100 , by what factor does the value of $\varepsilon / k_{B} T$ change at room temperature?