Q: A 1 kg sample of water is heated from $$20^\circC to$$ $$100^\circC at $$atmospheric pressure. If $$C_p = 4200 J K$^{-1}$$, what is the entropy change of the water?

$$\Delta S = 4200 \times \ln(373/293)$$

Question 1

Which statement best describes the Second Law of Thermodynamics as formulated by Kelvin?

Accepted Answer

It is impossible to convert all the heat absorbed from a hot reservoir into work in a cyclic process.

Question 2

A refrigerator operates between an inside temperature $$T_C$$ and an outside temperature $$T_H. $$Which of the following statements is correct?

Accepted Answer

Mechanical work must be supplied to transfer heat from the cold to the hot reservoir.

Question 3

For a Carnot engine operating between a hot reservoir at $$T_H$$ and a cold reservoir at $$T_C$$, which equation correctly relates the work output $$W to $$the heat flows?

Accepted Answer

$$W = |Q_H| - |Q_C|$$

Question 4

Which property of entropy makes it similar to internal energy $$U$$?

Accepted Answer

Entropy is a state function and its change depends only on the initial and final states.

Question 5

During a reversible isothermal expansion of an ideal gas, the change in entropy is given by:

Accepted Answer

$$\Delta S = \frac{Q_{rev}}{T}$$

Question 6

A Carnot cycle consists of two isothermal and two adiabatic processes. What is the total entropy change over one complete Carnot cycle?

Accepted Answer

$$\Delta S_{cycle} = 0$$

Question 7

A 1 kg sample of water is heated from $$20^\circC to$$ $$100^\circC at $$atmospheric pressure. If $$C_p = 4200 J K$^{-1}$$, what is the entropy change of the water?

Accepted Answer

$$\Delta S = 4200 	imes \ln(373/293)$$

Question 8

If the water in the previous question is heated irreversibly by a reservoir at $$100^\circC$$, what is the entropy change of the reservoir?

Accepted Answer

$$\Delta S_{reserv} = \frac{-Q_{received}}{T_{reserv}}$$

Question 9

According to the Principle of Increasing Entropy, what happens to the entropy of an isolated system during an irreversible process?

Accepted Answer

The entropy increases.

Question 10

Which equation expresses the Clausius inequality for any cyclic process?

Accepted Answer

$$\oint \frac{dQ}{T} \leq 0$$

Question 11

On a $$T$$-$$S$$ diagram, how is a reversible adiabatic process represented?

Accepted Answer

A line parallel to the $$T$$ axis (constant $$S)$$

Question 12

Which formula gives the microscopic definition of entropy according to Boltzmann?

Accepted Answer

$$S = k \ln w$$

Question 13

In the free expansion of $$n$$ moles of gas at temperature $$T to $$double its volume, what is the entropy change?

Accepted Answer

$$\Delta S = nR \ln 2$$

Question 14

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

Accepted Answer

Entropy provides a quantitative measure of disorder in a system.

Question 15

A process is reversible if:

Accepted Answer

It can be reversed without leaving any net change in the system and surroundings.

Question 16

Which statement about entropy in real-life scenarios is correct?

Accepted Answer

The explosion of a firecracker increases its disorder and entropy.

Question 17

If a system exchanges heat with a reservoir, which statement is true about the entropy change of the universe?

Accepted Answer

The total entropy change is positive for an irreversible process.

Question 18

Which of the following is NOT a property of entropy?

Accepted Answer

Entropy is path dependent.

Question 19

In a series of small reversible steps heating water from $$20^\circC to$$ $$100^\circC$$, which integral gives the entropy change?

Accepted Answer

$$\Delta S = mC_p \int_{T_i}^{T_f} \frac{dT}{T}$$

Question 20

Which scenario illustrates the concept of entropy as a measure of randomness?

Accepted Answer

Tossing a large number of coins, the most probable macro-state is half heads and half tails.

Entropy and the Second Law of Thermodynamics

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