Q: A 100 g block of ice at $$0^\circC is $$melted to liquid water at $$0^\circC. $$The heat of fusion is $$3.33 \times 10^5$ J/kg. What is the entropy change?

$$\Delta S = \frac{3.33 \times 10^4$ \text{ J}}{273 \text{ K}} = 122 \text{ J/K}$$

Q: A system consists of a 1.0 kg block of copper at $$20^\circC $$and a 1.5 kg block at $$300^\circC. $$The specific heat is $$385 J/kg$$·K. What is the final equilibrium temperature?

$$T_f = \frac{(1.0 \times 20) + (1.5 \times 300)}{1.0 + 1.5} = 184^\circC$

Question 1

For a monatomic ideal gas, what is the expression for the thermal energy $$E_{th} of$$ $$N$$ atoms at temperature $$T$$?

Accepted Answer

$$E_{th} = \frac{3}{2}Nk_BT$$

Question 2

A solid has six degrees of freedom per atom. Which of the following best explains why?

Accepted Answer

Each atom has three translational kinetic energy modes and three independent potential energy modes due to bonds.

Question 3

According to the equipartition theorem, how much energy is stored in each degree of freedom for $$N$$ particles at temperature $$T$$?

Accepted Answer

$$\frac{1}{2}Nk_BT$$

Question 4

Which of the following statements about heat transfer between two systems separated by a thin barrier is correct?

Accepted Answer

Energy is transferred via collisions until both systems reach the same average translational kinetic energy.

Question 5

A diatomic gas at room temperature has five degrees of freedom. Which modes are active?

Accepted Answer

Three translational and two rotational modes.

Question 6

Which law states that the entropy of an isolated system never decreases?

Accepted Answer

Second law of thermodynamics

Question 7

A block of ice melts at $$0^\circC to $$liquid water at $$0^\circC. $$What happens to the entropy of the water?

Accepted Answer

The entropy increases because the energy is more spatially dispersed in the liquid.

Question 8

What is the mathematical definition of entropy $$S$$ for a macrostate with multiplicity $$\Omega$$?

Accepted Answer

$$S = k_B \ln \Omega$$

Question 9

During a free expansion of a gas, what happens to the entropy and the ability to do work?

Accepted Answer

Entropy increases and the ability to do work decreases.

Question 10

For a slow isothermal process, what is the expression for the entropy change $$\Delta S$$?

Accepted Answer

$$\Delta S = \frac{Q}{T}$$

Question 11

A 100 g block of ice at $$0^\circC is $$melted to liquid water at $$0^\circC. $$The heat of fusion is $$3.33 	imes 10^5$ J/kg. What is the entropy change?

Accepted Answer

$$\Delta S = \frac{3.33 	imes 10^4$ 	ext{ J}}{273 	ext{ K}} = 122 	ext{ J/K}$$

Question 12

If the heat required to change the temperature of a solid of mass $$M$$ and specific heat $$c$$ from $$T_i to$$ $$T_f is$$ $$Q = Mc\Delta T$$, what is the entropy change?

Accepted Answer

$$\Delta S = Mc \ln \left( \frac{T_f}{T_i} \right)$$

Question 13

For an ideal gas, the entropy change for a constant-volume process is given by:

Accepted Answer

$$\Delta S = nC_V \ln \left( \frac{T_f}{T_i} \right)$$

Question 14

A system consists of a 1.0 kg block of copper at $$20^\circC $$and a 1.5 kg block at $$300^\circC. $$The specific heat is $$385 J/kg$$·K. What is the final equilibrium temperature?

Accepted Answer

$$T_f = \frac{(1.0 	imes 20) + (1.5 	imes 300)}{1.0 + 1.5} = 184^\circC$

Question 15

Which of the following best describes the third law of thermodynamics?

Accepted Answer

The entropy of a pure crystalline substance at absolute zero is zero.

Question 16

In the context of microstates and macrostates, what is the most probable macrostate for a large number of coins?

Accepted Answer

The macrostate with $$N/2$$ heads.

Question 17

Which process is irreversible according to the second law of thermodynamics?

Accepted Answer

Mixing cream into coffee.

Question 18

Which statement about entropy and disorder is most accurate?

Accepted Answer

Entropy is a measure of the spread or dispersal of energy, not disorder.

Thermal Energy, Specific Heat, and Entropy in Gases and Solids

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