Q: A 1 kg sample of water is heated from $$20^\circC to$$ $$100^\circC at $$atmospheric pressure. Given $$C_p = 4200 J K$^{-1}$$, what is the change in entropy of the water? (Use $$T_i = 293 K$$, $$T_f = 373 K)$$

$$\Delta S = 1 \times 4200 \times \ln(373/293) = 1013.9 J K$^{-1}$$

Question 1

A heat engine operates between a hot reservoir at temperature $$T_H$$ and a cold reservoir at temperature $$T_C. If $$the engine absorbs heat $$Q_H$$ from the hot reservoir and expels heat $$|Q_C| to $$the cold reservoir, what is the correct expression for the work $$W$$ done by the engine in one cycle?

Accepted Answer

$$W = Q_H - |Q_C|$$

Question 2

Which statement best describes the Kelvin-Planck formulation of the Second Law of Thermodynamics?

Accepted Answer

It is impossible to construct a device that operates in a cycle and produces no other effect than the transfer of heat from a single reservoir into work.

Question 3

A refrigerator removes heat $$Q_C$$ from its interior at temperature $$T_C$$ and expels heat $$Q_H to $$the room at temperature $$T_H. $$What is the minimum work $$W$$ required by the refrigerator per cycle?

Accepted Answer

$$W = Q_H - Q_C$$

Question 4

Which of the following is the correct mathematical definition of the infinitesimal change in entropy $$dS$$ for a reversible process?

Accepted Answer

$$dS = \frac{dQ_{rev}}{T}$$

Question 5

For a Carnot cycle operating between $$T_H$$ and $$T_C$$, which of the following is true for the total entropy change of the working substance after one complete cycle?

Accepted Answer

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

Question 6

A 1 kg sample of water is heated from $$20^\circC to$$ $$100^\circC at $$atmospheric pressure. Given $$C_p = 4200 J K$^{-1}$$, what is the change in entropy of the water? (Use $$T_i = 293 K$$, $$T_f = 373 K)$$

Accepted Answer

$$\Delta S = 1 	imes 4200 	imes \ln(373/293) = 1013.9 J K$^{-1}$$

Question 7

Which of the following statements about entropy is correct?

Accepted Answer

Entropy is a state function and its change depends only on the initial and final states, not the path taken.

Question 8

According to the microscopic interpretation, the entropy $$S of a $$macro-state is given by Boltzmann's formula. Which of the following is the correct expression?

Accepted Answer

$$S = k \ln w$$

Question 9

A gas undergoes a free expansion into a vacuum, doubling its volume at constant temperature. If the gas contains $$n$$ moles, what is the change in entropy of the gas?

Accepted Answer

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

Question 10

Which of the following best describes the Clausius statement of the Second Law of Thermodynamics?

Accepted Answer

No process is possible whose sole result is the transfer of heat from a colder body to a hotter body.

Question 11

If a system exchanges heat $$Q$$ with a reservoir at temperature $$T_{res}$$, what is the entropy change of the reservoir?

Accepted Answer

$$\Delta S_{reservoir} = -\frac{Q}{T_{res}}$$

Question 12

Which of the following is a correct statement of the Principle of Increasing Entropy?

Accepted Answer

In an isolated system, the total entropy can never decrease; it either increases (irreversible process) or remains constant (reversible process).

Question 13

On a $$T$$-$$S$$ diagram, which of the following correctly describes a reversible adiabatic process?

Accepted Answer

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

Question 14

Which of the following real-world scenarios best illustrates an increase in entropy?

Accepted Answer

A firecracker explodes, dispersing its contents randomly.

Question 15

For a reversible isothermal expansion of an ideal gas from volume $$V_i to$$ $$V_f at $$temperature $$T$$, what is the change in entropy of the gas?

Accepted Answer

$$\Delta S = nR \ln \frac{V_f}{V_i}$$

Question 16

A system undergoes a cyclic reversible process. What is the value of the integral $$\oint \frac{dQ_{rev}}{T}$$ over the cycle?

Accepted Answer

$$0$$

Question 17

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

Accepted Answer

Entropy is a quantitative measure of the number of possible microscopic arrangements (disorder) of a system.

Entropy and the Second Law of Thermodynamics: Study Notes

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