Question 1

A box of ideal gas molecules is divided in half by an imaginary line. Which macrostate is most likely?

Accepted Answer

The macrostate with the greatest number of possible microstates.

Question 2

What is the entropy $$S of a $$macrostate with 4 possible microstates? Use $$k_B$$ for Boltzmann's constant.

Accepted Answer

$$S = k_B \log 4$$

Question 3

Why can two systems with the same energy have different entropy?

Accepted Answer

Because entropy depends on the number of accessible microstates, not just energy.

Question 4

Which of the following best describes the relationship between entropy and reversibility?

Accepted Answer

A process is reversible if it does not increase the total entropy of the universe.

Question 5

A heat engine absorbs $$Q_H = 100\ \mathrm{J}$$ from a hot reservoir and does $$W_{out} = 40\ \mathrm{J} of $$work. What is its efficiency $$e$$?

Accepted Answer

$$e = 0.40$$

Question 6

Is a 100% efficient heat engine possible according to the second law of thermodynamics?

Accepted Answer

No, because some energy must always be expelled to a cold reservoir.

Question 7

The maximum theoretical efficiency of a heat engine operating between $$T_H$$ and $$T_C is $$given by:

Accepted Answer

$$e_{max} = 1 - \frac{T_C}{T_H}$$

Question 8

Which of the following changes would increase the maximum theoretical efficiency of a heat engine?

Accepted Answer

Increase $$T_H$$ and decrease $$T_C$$

Question 9

Why is the actual efficiency of real heat engines much less than the theoretical maximum?

Accepted Answer

Because of irreversibilities and energy losses such as friction and heat leaks.

Question 10

Which of the following is a biological example of a heat engine?

Accepted Answer

Early protocells converting chemical energy into work.

Question 11

The figure shows the potential energy $$U(x) of a $$system. At which point is the force $$F$$ the largest?

Accepted Answer

At the point where the slope of $$U(x) is $$steepest (largest $$|dU/dx|).$$

Question 12

The force $$F on a $$particle in a potential $$U(x) is $$zero at which point?

Accepted Answer

Where $$\frac{dU}{dx} = 0$$

Question 13

You flip a coin 5 times. Which outcome is most likely?

Accepted Answer

Any specific sequence (e.g., HTTHT) is equally likely as any other.

Question 14

Which of the following processes does NOT involve a change in entropy?

Accepted Answer

A ball rolls up a ramp, decreasing in speed as it rolls higher.

Question 15

A heat engine absorbs $$Q_H$$ from a hot reservoir at temperature $$T_H$$ and expels $$Q_C to a $$cold reservoir at $$T_C. $$Which equation correctly relates these quantities to the work output $$W_{out}$$?

Accepted Answer

$$W_{out} = Q_H - Q_C$$

Question 16

If a heat engine operates between $$T_H = 600\ \mathrm{K}$$ and $$T_C = 300\ \mathrm{K}$$, what is the maximum theoretical efficiency?

Accepted Answer

$$e_{max} = 1 - \frac{300}{600} = 0.5$$

Question 17

Which statement best explains why entropy increases in most natural processes?

Accepted Answer

Because there are more ways for energy to be disordered than ordered.

Question 18

A refrigerator is an example of which thermodynamic device?

Accepted Answer

A heat pump.

Question 19

Which of the following would NOT increase the entropy of a system?

Accepted Answer

Compressing a gas isothermally.

Heat Engines, Entropy, and the Second Law of Thermodynamics

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