Thermodynamics: notes and practice questions

A gas in a sealed container undergoes a process where $15.0\text{ J}$ of thermal energy is supplied to it, and $4.0\text{ J}$ of work is done on the gas.

What is the change in the internal energy of the gas?

A. $-19.0\text{ J}$

B. $-11.0\text{ J}$

C. $+11.0\text{ J}$

D. $+19.0\text{ J}$

A heat engine contains a fixed mass of an ideal gas as the working substance. The gas undergoes a cyclic process. In one cycle, the engine absorbs a quantity of thermal energy $Q_{\text{H}}$ from a hot source and expels a quantity of thermal energy $Q_{\text{C}}$ to a cold sink. The engine performs a net amount of work $W$. What is the net change in the internal energy of the gas for one complete cycle?

A. $W$

B. $Q_{\text{H}} - Q_{\text{C}}$

C. Zero

D. $Q_{\text{H}} + Q_{\text{C}}$

A proposed solar thermal power plant operates using a Carnot cycle. It generates an electrical output power of $150 \text{ MW}$. The plant extracts thermal energy from a high-temperature molten salt reservoir at $600^\circ\text{C}$ and rejects thermal energy to a cooling tower at $25^\circ\text{C}$.

(a) Calculate the rate of thermal energy supplied by the hot reservoir.

Consider a system of four coins. What is the entropy of a state in which two coins show heads and two coins show tails?

A. $k_\text{B} \ln(2)$

B. $k_\text{B} \ln(4)$

C. $k_\text{B} \ln(6)$

D. $k_\text{B} \ln(16)$

An ideal gas is the working substance for four different heat engines. The pressure-volume (P-V) diagrams for the cycles are shown. Each engine operates between the same two thermal reservoirs. Which cycle has the highest possible theoretical efficiency?

A.

B.

C.

D.

A fixed mass of an ideal gas undergoes the cyclic process A → B → C → D → A as shown in the pressure-volume (PV) diagram.

Which statement correctly describes the net work done ($W_{net}$) and the net thermal energy transferred ($Q_{net}$) during one complete cycle?

A. $W_{net}$ is done on the gas and $Q_{net}$ is transferred out of the gas.

B. $W_{net}$ is done by the gas and $Q_{net}$ is transferred into the gas.

C. $W_{net}$ is done on the gas and $Q_{net}$ is transferred into the gas.

D. $W_{net}$ is done by the gas and $Q_{net}$ is transferred out of the gas.

A sealed cylinder fitted with a movable piston contains an ideal monatomic gas. $120 \text{ J}$ of thermal energy is supplied to the gas, causing it to expand at a constant pressure of $1.5 \times 10^5 \text{ Pa}$. The volume of the gas increases from $4.0 \times 10^{-3} \text{ m}^3$ to $4.5 \times 10^{-3} \text{ m}^3$.

What is the change in the internal energy of the gas?

A. $45 \text{ J}$

B. $75 \text{ J}$

C. $120 \text{ J}$

D. $195 \text{ J}$

A sample of liquid water at its freezing point is placed in a freezer. The water turns into ice at a constant temperature.

What are the changes in the entropy of the water and the entropy of the freezer (the surroundings) during this process?

A sealed container holds a sample of an ideal monatomic gas. When the gas is at a temperature of $60$ °C, its internal energy is $5000$ J. $R$ is the gas constant.

How many moles of the gas are in the sample?

A. $\frac{6}{R}$

B. $\frac{10}{R}$

C. $\frac{15}{R}$

D. $\frac{500}{9R}$

A geothermal power plant operates with a hot reservoir (geothermal fluid) at a constant temperature. The cold reservoir is cooling water from a nearby river. When the river water temperature is $300$ K, the maximum theoretical (Carnot) efficiency of the plant is $0.40$.

Due to seasonal changes, the river water temperature drops to $150$ K. What is the new maximum theoretical efficiency of the plant?

A. $0.20$

B. $0.30$

C. $0.70$

D. $0.80$

Two identical, isolated systems, X and Y, each have an entropy of $S$ and a number of accessible microstates of $\Omega$. The two systems are brought into thermal contact to form a single combined system. What is the number of accessible microstates for the combined system?

A. $\Omega$

B. $2\Omega$

C. $\Omega^2$

D. $\sqrt{\Omega}$

An ideal gas and a real gas are at the same temperature and occupy the same volume. The number of particles in both gases is the same. How does the internal energy of the real gas, $U_{\text{real}}$, compare to the internal energy of the ideal gas, $U_{\text{ideal}}$?

A. $U_{\text{real}} > U_{\text{ideal}}$ because real gas particles have volume.

B. $U_{\text{real}} < U_{\text{ideal}}$ because there are attractive forces between real gas particles.

C. $U_{\text{real}} = U_{\text{ideal}}$ because temperature is the same.

D. The relationship cannot be determined without knowing the pressure.

An electric fan is operating inside a thermally insulated and sealed room.

The entropy of the air in the room

A. decreases.

B. remains unchanged.

C. increases.

D. is zero.

Cycle KLMK is composed of an isothermal, an adiabatic and an isovolumetric process.

What can be said about the change in internal energy and the sign of the work done by the gas in process LM?