Deck 6: Some Processes Are Irreversible Thermal Physics

Question 1

Consider a rectangular book. The book is (approximately) symmetric for rotations around an axis that goes diagonally from one corner to the other

Answer 1

T

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?

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

Answer 2

Its macrostate and macropartition

Question 3

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 of the combined system?

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

Answer 3

Its macrostate

Question 4

What is the crucial characteristic of an Einstein solid that makes it easier to analyze in the context of this chapter than most other kinds of thermodynamic systems?

A) The atoms are arranged in a regular, cubic lattice.
B) The atoms are identical.
C) Its microstates are comparatively easy to count.
D) Each atom's energy levels are equally spaced.
E) $\Omega(U, N)$ is always reasonably small.
F) Other (specify).

Question 5

We can ignore an Einstein solid's zero-point energy because

A) it is zero.
B) it never changes in any thermal interaction.
C) it is insignificant compared to the solid's total energy.
D) it is just a quantum-mechanical effect.
E) other (specify).

Question 6

Which of the following statements is true?

A) There are always many microstates in a macrostate.
B) All accessible macrostates are equally probable.
C) All microstates of a system are equally probable.
D) All accessible macropartitions are equally probable.
E) When two objects in thermal contact are isolated from everything else, their macrostates cannot change.
F) None of the above.

Question 7

Suppose that we increase an $N$ -atom Einstein solid's value of $q=U / \varepsilon$ from $q$ to $q+1$ . By what factor does the value of its multiplicity $\Omega$ increase? (Choose whichever result is the closest, assuming that $q>>1$ and $N>>1$ .)

A) $q$
B) $3 N$
C) $q / 3 N$
D) $3 N / q$
E) $(q+3 N) / q$
F) $(q+3 N) /(q N)$

Question 8

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 $U$ ?

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 9

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.

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 10

Consider the system where $N_{A}=N_{B}=1000, U=5999 \varepsilon$ (see figure T2.6). Suppose that we can measure each object's energy to within $0.01 U \approx 60 \varepsilon$ (the size of one bin). Once the system has reached a macropartition in the most probable bin, it will never spontaneously move to a macropartition outside that bin.

Question 11

Which of the systems listed below is the largest, having $N_{A}=N_{B}$ and $U=6 N_{A} \varepsilon$ for which there is a better than 1 in a billion chance of seeing one or the other solid having zero energy? (Hint: Using StatMech to check cases is probably the easiest approach.)

A) $N_{A}=6$
B) $N_{A}=8$
C) $N_{A}=10$
D) $N_{A}=12$
E) $N_{A}=15$

Question 12

A hot object is placed in contact with a cold object. We observe that heat flows spontaneously from the hot object to the cold object, but not in the other direction. According to the argument in this chapter, this is so because

A) this increases the entropies of both objects.
B) this decreases the entropy of the combined system.
C) the system will tend to evolve toward macropartitions that have more microstates.
D) $A$ and $C$
E) $B$ and $C$

Question 13

Consider an object (object $A$ ) whose multiplicity is always 1 , no matter how much energy you put into it. If you put a very large amount of energy into such an object, and place it into thermal contact with an Einstein solid (object $B$ ) having the same number of atoms but much less energy, what will happen? (Hint: Imagine a macropartition table for such a pair of objects.)

A) Energy flows from $A$ to $B$ until $A$ has very little energy.
B) Energy flows from $B$ to $A$ until $B$ has very little energy.
C) Energy flows from $A$ to $B$ until both objects have the same energy.
D) No energy will flow between $A$ and $B$ at all.
E) Something else happens (describe).

Question 14

In a given macropartition, the total entropy of a system comprised of two or more parts is always equal to the sum of the entropies of those parts.

Question 15

$10^{62} / 10^{60}=100$ . What is $\ln 10^{62} /$ In $10^{60}$ ? (Select the closest response.)

A) 100
B) 10
C) 4.6
D) $\mathbf{1 . 0}$

Question 16

The entropy of a certain macropartition of a combined system is $102 \mathrm{k}_{\mathrm{B}}$ . The entropy of another macropartition is $204 \mathrm{k}_{\mathrm{B}}$ . How much more likely is the system to be in the second macropartition than the first? (Select the closest response.)

A) 2 times
B) $\mathrm{e}^{2}=7.4$ times
C) $10^{2}=100$ times
D) $\mathrm{e}^{102}=2 \times 10^{44}$ times
E) $e^{102 k_{B}} \approx e^{0}$ ; so the two macropartitions have basically the same probability

Question 17

Which system has the greater entropy, a puddle of water sitting on a table next to a chaotic scattering of salt crystals or the same amount of salt dissolved in an evenly distributed way in the puddle? Be prepared to describe your reasoning.

A) The puddle and the scattered crystals.
B) The puddle with the dissolved salt.
C) Both have the same entropy.
D) One needs detailed models of water and salt to say.

Question 18

Object A's entropy increases quite a bit when we give it a certain tiny amount of energy, whereas object B's entropy increases by a much smaller amount with the same gift. Which has the higher temperature?

A) Object $A$
B) Object $B$
C) One cannot say without more information.

Question 19

As a normal object's thermal energy $U$ goes to zero, the slope of a graph of its entropy $S$ versus $U$

A) approaches infinity.
B) approaches some positive value less than infinity.
C) approaches zero.
D) approaches some finite negative value.
E) approaches negative infinity.
F) depends entirely on the object's properties.

Question 20

Consider a system whose multiplicity is 1 , no matter how much energy one puts into it. What is such a system's temperature?

A) Zero
B) Positive
C) Negative
D) Undefined

Question 21

Suppose that an object's entropy increases from zero when its thermal energy is $U=0$ to some maximum value when $U=\frac{1}{2} U_{\text {max }}$ , and then goes back to zero when $U=U_{\max }$ (as shown in the drawing below). The greatest thermal energy $U$ that such an object could have when in thermal equilibrium with a normal object is closest to which of the following?

A) 0
B) $\frac{1}{4} U_{\max }$
C) $\frac{1}{2} U_{\max }$
D) $\frac{3}{4} U_{\max }$
E) $U_{\max }$
F) Other (specify)

Question 22

If an object has a multiplicity $\Omega$ that decreases as its thermal energy $U$ increases, its temperature would

A) be always zero.
B) be always positive (and nonzero).
C) be negative (and nonzero).
D) increase as $U$ increases.
E) decrease as $U$ increases.

Question 23

Suppose that an atom has two energy levels separated by an energy difference $\Delta E$ . When such atoms are in thermal contact with a reservoir at temperature $T$ , there is roughly 1 atom in the higher state for every 4 in the lower state. What is the approximate ratio of $\Delta E$ to $k_{B} T$ ?

A) $\frac{1}{4}$
B) 4
C) In 4
D) $-\ln 4$
E) $e^{-1 / 4}$
F) $e^{-4}$
G) Other (specify)

Question 24

Suppose that an atom has exactly two energy levels separated by an energy difference $\Delta \mathrm{E}$ . When such atoms are in contact with a reservoir at a temperature $T_{1}$ , the ratio of the number of atoms in the higher level to the number in the lower level is $\frac{1}{4}$ . If we increase the temperature to $T_{2}$ , the numerical value of this ratio

A) increases.
B) decreases.
C) remains the same.

Question 25

The quantity $Z$ in the expression $\operatorname{Pr}(\mathrm{E})=\mathrm{Z}^{-1} \mathrm{e}^{-\mathrm{E} / \mathrm{k}_{\mathrm{B}} \mathrm{T}}$ depends on the temperature $T$ of the reservoir.

Question 26

The quantity $Z$ in the expression $\operatorname{Pr}(E)=Z^{-1} e^{-E / k_{B} T}$ must be

A) always greater than 1 .
B) always less than 1 .
C) It could be either greater than or less than 1.

Question 27

As temperatures become large, the denominator in equation $\mathrm{T} 4.36$ becomes
Equation $\mathrm{T} 4.36$
$U=3 N E_{\text {avg }}=\frac{3 N \varepsilon e^{-\varepsilon / k_{B} T}}{1-e^{-\varepsilon / k_{B} T}}=\frac{3 N \varepsilon}{e^{\varepsilon / k_{B} T}-1}$

A) very large.
B) very small.
C) approximately 1.
D) approximately -1 .

Question 28

Suppose that the energy difference between adjacent energy levels for an oscillator in an Einstein solid is $\varepsilon=$ $0.005 \mathrm{eV}$ . At room temperature, the value of $T / T_{E}$ is

A) quite a bit smaller than 1
B) about equal to 0.5 .
C) about equal to 1 .
D) about equal to 2 .
E) quite a bit larger than 2.
F) (One doesn't have enough information to tell.)

Question 29

Suppose that the energy difference between adjacent energy levels for an oscillator in an Einstein solid is $\varepsilon=$ $0.005 \mathrm{eV}$ . We would expect the average energy of this oscillator when it is in contact with a reservoir at room temperature to be

A) negligible.
B) smaller than $\frac{1}{2} k_{B} T$ .
C) about equal to $\frac{1}{2} k_{B} T$ .
D) about equal to $k_{B} T$ .
E) significantly larger than $k_{B} T$ .
F) One doesn't have enough information to tell.

Question 30

To calculate an object's heat capacity, we take its specific heat and

A) multiply by the object's mass $M$ .
B) divide by the object's mass $M$ .
C) multiply by the molar mass $M_{A}$ of the object's molecules.
D) divide by the molar mass $M_{A}$ of the object's molecules.
E) multiply by the mass $m$ of one molecule in the object.
F) divide by the mass $m$ of one molecule in the object.
G) do something else (specify).

Question 31

Suppose that the temperature $T$ is about $T_{E} / 9$ for a certain Einstein solid. The probability that an oscillator in that solid will have one unit of energy is closest to
(Hint: See equation $T 4.32$ for how to calculate $Z$ .)
Equation T4.32:
$$1+x+x^{2}+\ldots=\frac{1}{1-x}$$

A) 1
B) $1 / 9$
C) $1 / 81$
D) $1 / 8000$
E) $1 / 10^{9}$

Question 32

$T_{E}$ is much smaller for lead than for iron. Which therefore has the greater heat capacity per atom at

-(a) $T=100 \mathrm{~K}$ ?

A) Lead
B) Iron
C) Both should be about the same.

Question 33

$T_{E}$ is much smaller for lead than for iron. Which therefore has the greater heat capacity per atom at

-(b) $T=400 \mathrm{~K}$ ?

A) Lead
B) Iron
C) Both should be about the same.

Question 34

At a sufficiently high temperature, an oscillator in an Einstein solid is more likely to have one unit of energy than no energy at all.

Question 35

Suppose that the forces holding an atom in its position in a crystal are the same for two different monatomic solids, but the mass of an atom $m$ is larger for solid $B$ than for solid $A$ . Which has the larger value of $T_{E}$ ?

A) Solid $A$
B) Solid $B$
C) Both have about the same value of $T_{E}$ .

Question 36

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?

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

Question 37

Using an integral to calculate a sum over $f(n)$ (where $n$ is an integer) is a good approximation when

A) the summed values $f(n)$ are individually small.
B) the value of $\boldsymbol{f}(\boldsymbol{n})$ varies only very slowly with $\boldsymbol{n}$ .
C) the value of $f(n)$ goes to zero as $n$ goes to infinity.
D) the value of $f(n)$ goes to zero as $n$ goes to zero.
E) All of the conditions above are true.

Question 38

Which of the following energy storage modes for a gas molecule "switch on" fully at

-(a) the lowest temperature?

A) The molecule's kinetic energy
B) The molecule's rotational energy
C) The molecule's vibrational energy

Question 39

Which of the following energy storage modes for a gas molecule "switch on" fully at

-(b) the highest temperature?

A) The molecule's kinetic energy
B) The molecule's rotational energy
C) The molecule's vibrational energy

Question 40

The heat capacity of any energy storage mode with quantized energy levels goes to zero as the temperature $T$ goes to zero.

Question 41

An atom of helium can store energy by bumping an electron from its lowest orbital energy state to a higher orbital energy level. In particular, moving an electron from the lowest state to the next-lowest state would store an energy of $24.6 \mathrm{eV}$ . Why can we ignore this energy storage mode when calculating the heat capacity of helium gas?

A) This mode is "frozen" out at normal temperatures.
B) Collisions between atoms can't influence the energy levels of electrons inside the atoms.
C) This storage mode is completely independent of the kinetic and/or rotational energy modes.
D) Only modes involving helium molecules count.
E) We have ignored this mode only for simplicity's sake.
F) Some other reason (specify).

Question 42

(a) The average $x$ -velocity of molecules in a container of gas at rest is zero.

Question 43

(b) The average molecular speed is zero.

Question 44

If the speed of a molecule in a container doubles (other things remaining the same), the average pressure that this molecule exerts on the container wall

A) remains the same.
B) doubles.
C) quadruples.
D) One does not have enough information to say.

Question 45

Suppose that when we add $20.8 \mathrm{~J}$ to 1 mol of a certain gas, its temperature is observed to increase by $1 \mathrm{~K}$ . Which of the following statements is true?

A) This gas is monatomic.
B) This gas is diatomic.
C) This gas is polyatomic.
D) One cannot determine the type of gas without information that we are not given.
E) The results described are impossible.

Question 46

The ideal gas model assumes that molecules have infinitesimal size. Consider one molecule bouncing around in the container. As the molecule's size increases relative to the size of the container, how will the average pressure $P$ that it exerts change, other things being held constant?

A) $\boldsymbol{P}$ increases.
B) $P$ does not change.
C) $P$ decreases.
D) One does not have enough information to say.

Question 47

Two identical rooms, $A$ and $B$ , are sealed except for an open doorway between them. Room $A$ is warmer than $B$ . Which room has the greater number of molecules? (Hint: How will the pressures in the two rooms compare?)

A) Room A
B) Room B
C) Both have the same number of molecules.

Question 48

One mole of hydrogen gas and $\frac{1}{2}$ mole of helium gas are mixed in a container and maintained at a fixed temperature $T$ . How does the total pressure $P_{\mathrm{H}}$ exerted by the hydrogen molecules compare to the total pressure $P_{\mathrm{He}}$ exerted by the helium molecules? Note that a molecule (atom) of helium has twice the mass of an $\mathrm{H}_{2}$ molecule.

A) $P_{\mathrm{H}}=2 P_{\mathrm{He}}$
B) $P_{\mathrm{H}}=\sqrt{2} P_{\mathrm{He}}$
C) $P_{\mathrm{H}}=P_{\mathrm{He}}$
D) $P_{\mathrm{H}}=\sqrt{\frac{1}{2}} P_{\mathrm{He}}$
E) $P_{\mathrm{H}}=\frac{1}{2} P_{\mathrm{He}}$
F) Other (specify)

Question 49

$N$ 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.

-(a) the greater value of $\left[v^{2}\right]_{\text {avg }}$ ,

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 50

$N$ 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.

-(b) the greater average kinetic energy per molecule,

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 51

$N$ 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

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 52

$N$ 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.

-(d) the greater pressure $P$ ?

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 53

When counting particle-in-a-box quantum states in three dimensions, why do we divide the "volume" of only one eighth of a full spherical shell by the "volume" per quantum state? Why not the full shell's volume?

A) Molecules in a gas can only have positive momentum components.
B) A single quantum energy state embraces both positive and negative values for each momentum component.
C) A particle's momentum magnitude must be positive.
D) The factor of 2 in the expression $h / 2 L$ already counts both possible momentum signs.
E) We really do include the full shell: the diagram only shows $1 / 8$ of the shell to make it easier to draw.
F) Some other reason (specify).

Question 54

Physically, why is a gas molecule's speed $v$ more likely to be near $v_{p}$ than near zero?

A) There are fewer quantum states with smaller speeds than larger speeds.
B) The Boltzmann factor has a larger value near $\mathrm{v}=\mathrm{v}_{\mathrm{p}}$ than near $v=0$ .
C) We know that $\frac{1}{2} m\left[v^{2}\right]_{\text {avg }}=\frac{3}{2} k_{B} T$ , and $v_{p}$ is closer to $\left[v_{\text {avg }}^{2}\right]^{1 / 2}$ than zero is.

Question 55

Physically, why is a gas molecule's speed $v$ more likely to be near $v_{p}$ than near $2 v_{p}$ ?

A) There are fewer quantum states for larger speeds than there are at speeds near $v_{p}$ .
B) The Boltzmann factor is larger at $\mathbf{v}_{\mathbf{p}}$ than at $\mathbf{2} \mathbf{v}_{\mathbf{p}}$ .
C) We know that $\frac{1}{2} m\left[v^{2}\right]_{\text {avg }}=\frac{3}{2} k_{B} T$ , and $\mathrm{v}_{\mathrm{p}}$ is closer to $\left[v_{\text {avg }}^{2}\right]^{1 / 2}$ than $2 \mathrm{v}_{\mathrm{p}}$ is.

Question 56

How should $\left(\left[v^{3}\right]_{\text {avg }}\right)^{1 / 3}$ compare to $\left(\left[v^{2}\right]_{\text {avg }}\right)^{1 / 2}$ for an ideal gas?

A) $\left(\left[v^{3}\right]_{\text {avg }}\right)^{1 / 3}>\left(\left[v^{2}\right]_{\text {avg }}\right)^{1 / 2}$
B) $\left(\left[v^{3}\right]_{\text {avg }}\right)^{1 / 3}=\left(\left[v^{2}\right]_{\text {avg }}\right)^{1 / 2}$
C) $\left(\left[v^{3}\right]_{\text {avg }}\right)^{1 / 3}<\left(\left[v^{2}\right]_{\text {avg }}\right)^{1 / 2}$
D) One cannot tell without careful calculation.

Question 57

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 $v=v_{p}$ ).

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

Question 58

How would the values of $\mathrm{v}_{\mathrm{p}}$ for carbon dioxide gas compare to that of nitrogen gas at a given temperature? (Hint: Carbon dioxide gas has a molar mass of $44 \mathrm{~g} / \mathrm{mole}$ ; nitrogen has a molar mass of $28 \mathrm{~g} / \mathrm{mole}$ .)

A) $v_{p}$ will be larger for carbon dioxide.
B) $v_{p}$ will be larger for nitrogen.
C) $v_{p}$ will be equal in both cases.
D) One does not have enough information to tell for sure.

Question 59

How does the number of molecules with speed $v\left\langle v_{P}\right.$ compare to the number having speed $v>v_{P}$ ?

A) Fewer molecules have $v>v_{P}$ .
B) The same number of molecules are in each range.
C) More molecules have $v>v_{P}$ .
D) The answer depends on the temperature.

Question 60

The number of photons per second radiated by a blackbody is proportional to what power of $T$ ?

A) $T$
B) $T^{2}$
C) $T^{3}$
D) $T^{4}$
E) $T^{5}$

Question 61

Doubling a blackbody's temperature doubles the number of photons it emits per second.

Question 62

Will a blackbody at temperature $T$ emit more photons per second with energy $0.5 k_{B} T$ or with energy $1.5 k_{B} T$ ? (Note: The amount of energy emitted per time is not the same as the number of photons emitted per time, though these quantities are related.)

A) It will emit more photons with the lower energy.
B) It will emit more photons with the higher energy.
C) The number of photons emitted will be the same.
D) One has no way of telling.

Question 63

Will a blackbody at temperature $T$ emit more photons-perBsecond with energy $k_{B} T$ or with energy $6 k_{B} T$ ? (Note: The amount of energy emitted per time is not the same as the number of photons emitted per time, though these quantities are related.)

A) It will emit more photons with the lower energy.
B) It will emit more photons with the higher energy.
C) The number of photons emitted will be the same.
D) One has no way of telling.

Question 64

A perfectly reflective piece of metal at room temperature would not radiate any photons,

Question 65

An object strongly reflects red light, but readily absorbs all other colors of light. Relative to the number of thermal photons of red light emitted by a black body at the same temperature $T$ , our object's thermal emission rate of photons of red light will be

A) enhanced.
B) Suppressed.
C) unchanged.
D) The answer depends on the value of $T$ .

Question 66

Suppose that a star has twice the surface temperature of the sun and also twice the radius. How many times larger is the rate at which this star emits energy compared to the rate at which the sun emits energy?

A) The star radiates at the same rate as the sun.
B) 2 times
C) 4 times
D) 8 times
E) 16 times
F) 32 times
G) 64 times

Question 67

Suppose that we double the electrical power flowing into the filament of an incandescent bulb. By what factor will the most probable photon energy $\varepsilon_{p}$ increase?

A) $2^{1 / 4}$
B) $2^{1 / 3}$
C) $2^{1 / 2}$
D) 2
E) 4
F) 8
G) 16

Question 68

A gas with a pressure of $100 \mathrm{kPa}$ is in a container that is a cube measuring $10 \mathrm{~cm}$ on a side. If we move one wall in 1 millimeter ( $\mathrm{mm}$ ), does work flow into (A) or out of (B) the gas? What is the magnitude of W?

A) $1000 \mathrm{~J}$
B) $100 \mathrm{~J}$
C) $10 \mathrm{~J}$
D) $1 \mathrm{~J}$
E) $0.001 \mathrm{~J}$
F) Other (specify)

Question 69

Which of the following triplets of macroscopic variables would not adequately specify a gas's macrostate?

A) $U, V, T$
B) $P, T, N$
C) $U, N, T$
D) $M, V, T$
E) $M, P, V$
F) $M, P, U$

Question 70

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process:


-The process $B \rightarrow C$ shown is

A) an isochoric process.
B) an isothermal process.
C) an isobaric process.
D) an adiabatic process.
E) an isometric process.
F) none of the above.

Question 71

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 $A \rightarrow B$ ?

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

Question 72

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 $B \rightarrow C$ ?

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

Question 73

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 $C \rightarrow A$ ?

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

Question 74

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process:


-In static equilibrium, any excess charge on a conductor is uniformly spread on its surface.

Question 75

Problems T7T. 3 through T7T. 7 refer to the following cyclic gas process:


-When an object slides down a frictionless incline, The interaction does not change the object's momentum

Question 76

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)?

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

Question 77

If the temperature of the bubble described in problem T7T. 8 was $320 \mathrm{~K}$ when it formed, what is its approximate final temperature when it reaches the surface?

A) $40 \mathrm{~K}$
B) $80 \mathrm{~K}$
C) $320 \mathrm{~K}$
D) $1280 \mathrm{~K}$
E) $2560 \mathrm{~K}$
F) Other (specify)

Question 78

During an adiabatic compression, does a gas's temperature increase, decrease, or remain the same?

A) It increases.
B) It decreases.
C) It remains the same.

Question 79

Does the pressure of a gas decrease more rapidly or less rapidly when expanding adiabatically than it would when expanding isothermally?

A) More rapidly.
B) Less rapidly.
C) The pressure decreases at the same rate in both cases.
D) The pressure increases in an adiabatic expansion.
E) The pressure increases in an isothermal expansion.

Question 80

Water actually contracts when it is warmed near its freezing point. In this range, is water's heat capacity at constant volume (A) greater than, (B) less than, or (C) equal to its heat capacity at constant pressure?

A) greater than
B) less than
C) equal to