Q: Which equation correctly expresses the first law of thermodynamics for a heat engine cycle?

$Q = W + \Delta E_{\text{int}}$

Q: A steam power plant operates between $T_H = 673\,\mathrm{K}$ and $T_C = 298\,\mathrm{K}$. What is the maximum possible efficiency for converting heat to electric energy?

$\eta_{\text{max}} = 1 - \frac{298}{673} \approx 0.56$

Q: Which of the following is true for a Carnot refrigerator operating between $T_H$ and $T_C$?

Its coefficient of performance is $K_{\text{Carnot}} = \frac{T_C}{T_H - T_C}$.

Q: A Brayton-cycle refrigerator operates between $T_H = 381\,\mathrm{K}$ and $T_C = 250\,\mathrm{K}$. What is the maximum possible coefficient of performance for a Carnot refrigerator operating between these temperatures?

$K_{\text{Carnot}} = \frac{250}{381 - 250} \approx 1.91$

Question 1

Which statement best describes the second law of thermodynamics as it applies to heat engines?

Accepted Answer

No heat engine operating between two reservoirs can be more efficient than a Carnot engine operating between those same reservoirs.

Question 2

A refrigerator removes 2000 J of heat from its cold reservoir and requires 800 J of work input. What is its coefficient of performance $K$?

Accepted Answer

$K = \frac{2000}{800} = 2.5$

Question 3

Which of the following processes is an example of an irreversible process?

Accepted Answer

A car crash.

Question 4

A Carnot engine operates between a hot reservoir at $T_H = 600\,\mathrm{K}$ and a cold reservoir at $T_C = 300\,\mathrm{K}$. What is its maximum possible efficiency $\eta_{	ext{Carnot}}$?

Accepted Answer

$\eta_{	ext{Carnot}} = 0.5$

Question 5

Which equation correctly expresses the first law of thermodynamics for a heat engine cycle?

Accepted Answer

$Q = W + \Delta E_{	ext{int}}$

Question 6

A steam power plant operates between $T_H = 673\,\mathrm{K}$ and $T_C = 298\,\mathrm{K}$. What is the maximum possible efficiency for converting heat to electric energy?

Accepted Answer

$\eta_{	ext{max}} = 1 - \frac{298}{673} \approx 0.56$

Question 7

Which statement about entropy is correct?

Accepted Answer

Entropy is a measure of disorder; it tends to increase in spontaneous processes.

Question 8

A gasoline engine in a car has a thermal efficiency of 25%. If the engine absorbs $Q_H = 4000\,\mathrm{J}$ of heat from the hot reservoir, how much work does it perform per cycle?

Accepted Answer

$W = 1000\,\mathrm{J}$

Question 9

Which of the following is true for a Carnot refrigerator operating between $T_H$ and $T_C$?

Accepted Answer

Its coefficient of performance is $K_{	ext{Carnot}} = \frac{T_C}{T_H - T_C}$.

Question 10

A heat engine absorbs $Q_H = 5000\,\mathrm{J}$ from the hot reservoir and exhausts $Q_C = 3500\,\mathrm{J}$ to the cold reservoir per cycle. What is its thermal efficiency?

Accepted Answer

$\eta = \frac{1500}{5000} = 0.3$

Question 11

Which of the following statements about real heat engines is correct?

Accepted Answer

Real heat engines always exhaust some energy as waste heat to the environment.

Question 12

In a Carnot cycle, during which processes is heat transferred?

Accepted Answer

During the two isothermal processes only.

Question 13

A Brayton-cycle refrigerator operates between $T_H = 381\,\mathrm{K}$ and $T_C = 250\,\mathrm{K}$. What is the maximum possible coefficient of performance for a Carnot refrigerator operating between these temperatures?

Accepted Answer

$K_{	ext{Carnot}} = \frac{250}{381 - 250} \approx 1.91$

Question 14

Which of the following is a necessary condition for a system to be considered an energy reservoir?

Accepted Answer

Its temperature remains constant when heat is transferred to or from it.

Question 15

A heat engine absorbs $Q_H$ from a hot reservoir and exhausts $Q_C$ to a cold reservoir. Which formula gives the work done per cycle?

Accepted Answer

$W = Q_H - Q_C$

Question 16

Which of the following would violate the second law of thermodynamics?

Accepted Answer

A refrigerator that moves heat from cold to hot without any work input.

Question 17

If a Carnot engine has a cold reservoir at $T_C = 283\,\mathrm{K}$ and you want an efficiency of $0.7$, what must the temperature of the hot reservoir $T_H$ be?

Accepted Answer

$T_H = \frac{T_C}{1 - \eta} = \frac{283}{0.3} \approx 943\,\mathrm{K}$

Question 18

Which of the following is a correct statement about the arrow of time in thermodynamics?

Accepted Answer

The direction in which entropy increases is defined as the future.

Question 19

Which of the following is true for the efficiency of a real engine compared to a Carnot engine operating between the same reservoirs?

Accepted Answer

The real engine's efficiency is always less than the Carnot efficiency.

Heat Engines and Refrigerators: Principles and Applications (Chapter 21 Study Notes)

Study Guide - Practice Questions

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