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. -(c) A tornado

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?

Which of the following statements is true?

The model we have constructed in this chapter neglects feedback effects that might accelerate or brake the warming. Scientists now predict that the Arctic Ocean will be ice-free in the summer by as early as 2020 (due to increased temperatures in the Arctic). Less ice will mean that the Arctic will reflect less visible light back into space. Will this accelerate or brake the warming compared to the predictions of the model in the text?

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?

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!) -(e) A cube of ice melts in a glass sitting on a table.

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

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

Someone comes to your house selling a device that draws heat from groundwater and supplies that heat to your house. The salesperson claims that the amount of heat energy entering the house will far exceed the electrical energy supplied to the device. What the salesperson claims here is physically impossible.

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)? -Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. Their inner product $\langle u \mid w\rangle$ is a real number.

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 $28 \mathrm{~g} / \mathrm{mole}$ .)

Is pressure a?

Suppose scientists discover (somehow) that if $\Delta T$ , the average global temperature increase since 1900, were to exceed $1.0^{\circ} \mathrm{C}$ , Greenland's ice sheet would irreversibly start to collapse within 20 years, raising ocean levels significantly. $\Delta T$ is currently $0.8^{\circ} \mathrm{C}$ . What might we do to prevent this from happening?

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 sample of helium gas with an initial temperature of $T_{i}$ in an insulated cylinder with initial volume $V_{i}$ is suddenly and violently compressed to one-half its volume. The absolute temperature of the gas after the compression is observed to have doubled. (Note: In a quasistatic adiabatic compression of a monatomic gas, $\mathrm{TV}^{2 / 3}=$ constant.) A suitable replacement process for this process would be

The model we have constructed in this chapter neglects feedback effects that might accelerate or brake the warming. It is possible that higher temperatures will yield increased evaporation and increased cloud cover. Will this accelerate or brake the warming compared to the predictions of the model in the text?

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?)

Characterize each of the following processes as being reversible (A) or irreversible (B). (Some answers may be debatable!) -(d) A piece of hamburger meat cooks on a grill.

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

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?