Exam 6: Some Processes Are Irreversible Thermal Physics

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!) -(c) A ball rebounds elastically from a wall.

Which of the following energy storage modes for a gas molecule "switch on" fully at -(b) the highest temperature?

Suppose that, in Iceland, scientists discover geothermal vents that produce pressurized steam at $300^{\circ} \mathrm{C}$ . Engineers construct a heat engine that uses this steam as a hot reservoir and a nearby glacier as a cold reservoir. What is the maximum possible efficiency of this engine?

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

Suppose you stretch a rubber band. The work you do on the rubber band is

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?

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

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

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

$T_{E}$ is much smaller for lead than for iron. Which therefore has the greater heat capacity per atom at -(b) $T=400 \mathrm{~K}$ ?

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.)

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.)

Classify the following hypothetical perpetual motion machines as being perpetual motion machines of the first kind $(A)$ or the second kind (B). -(d) Compressed air from a tank blows on a windmill. The windmill is connected to a generator that produces electrical energy. Part of that electrical energy is used to compress more air into the tank.

$N$ 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 $\left[v^{2}\right]_{\text {avg }}$ ,

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?

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

To function, a home air conditioning system must have access to the home's exterior.

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)? -

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