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

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

Question 1

Which of the following best describes the micro/macro connection in thermodynamics?

Accepted Answer

It relates the macroscopic properties of a system to the motion and collisions of its atoms and molecules.

Question 2

The pressure in a gas is primarily due to:

Accepted Answer

The collisions of the molecules with the walls of the container.

Question 3

What is the root-mean-square (rms) speed $$v_{rms} of $$molecules in a gas of mass $$m at $$temperature $$T$$?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$

Question 4

The average translational kinetic energy of a molecule in an ideal gas is given by:

Accepted Answer

$$\epsilon_{avg} = \frac{3}{2} k_B T$$

Question 5

A sealed, insulated container has 2.0 g of helium at 300 K and 10.0 g of argon at 600 K separated by a thin barrier. After thermal equilibrium is reached, which statement is correct?

Accepted Answer

Heat is transferred from argon to helium until both reach the same final temperature.

Question 6

The mean free path $$\lambda of a $$molecule in a gas is given by:

Accepted Answer

$$\lambda = \frac{1}{4 \sqrt{2} \pi r^2$ (N/V)}$$

Question 7

According to the equipartition theorem, the thermal energy of a system of $$N$$ particles at temperature $$T$$ with $$f$$ degrees of freedom is:

Accepted Answer

$$E_{th} = \frac{f}{2} N k_B T$$

Question 8

Which of the following statements about entropy is correct?

Accepted Answer

Entropy is a state variable that measures the number of ways a macrostate can be arranged microscopically.

Question 9

For a slow, reversible transfer of heat $$dQ at $$temperature $$T$$, the change in entropy $$dS is$$:

Accepted Answer

$$dS = \frac{dQ}{T}$$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

Heat flowing spontaneously from a hot object to a cold object.

Question 12

The entropy $$S of a $$macrostate with multiplicity $$\Omega is $$given by:

Accepted Answer

$$S = k_B \ln \Omega$$

Question 13

For a monatomic ideal gas, the molar specific heat at constant volume $$C_V is$$:

Accepted Answer

$$C_V = \frac{3}{2} R$$

Question 14

If the volume of an ideal gas doubles during a slow (quasi-static) isothermal expansion, the entropy change is:

Accepted Answer

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

Question 15

Which of the following best explains why the molar specific heat is the same for all monatomic gases?

Accepted Answer

All monatomic gases have three translational degrees of freedom, so energy is distributed equally among them.

Question 16

A diatomic gas at room temperature has how many degrees of freedom contributing to its thermal energy?

Accepted Answer

Five (three translational and two rotational)

Question 17

Which of the following is a correct statement of the second law of thermodynamics?

Accepted Answer

The entropy of an isolated system never decreases; it increases until equilibrium is reached.

Question 18

The multiplicity $$\Omega of a $$system with $$N$$ molecules in volume $$V is $$given by:

Accepted Answer

$$\Omega = cV^N$$

Question 19

Which of the following best describes thermal equilibrium between two systems?

Accepted Answer

Both systems have the same average translational kinetic energy per molecule.

The Micro/Macro Connection: Statistical Physics and Thermodynamics

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