Q: A system has $W = 1.0 \times 10^{23}$ microstates. Using the Boltzmann equation, what is the entropy of the system? ($k = 1.38 \times 10^{-23}\ \mathrm{J/K}$)

$S = 7.3 \times 10^{-22}\ \mathrm{J/K}$

Question 1

According to the Third Law of Thermodynamics, what is the entropy of a perfect crystal at absolute zero ($0\ \mathrm{K}$)?

Accepted Answer

$S = 0$

Question 2

Which of the following statements about microstates is INCORRECT?

Accepted Answer

A perfect crystal at $0\ \mathrm{K}$ has a number of microstates greater than 1.

Question 3

The Boltzmann equation for entropy is given by $S_{sys} = k \ln W$. What does $W$ represent in this equation?

Accepted Answer

The number of microstates available to the system.

Question 4

A system has $W = 1.0 	imes 10^{23}$ microstates. Using the Boltzmann equation, what is the entropy of the system? ($k = 1.38 	imes 10^{-23}\ \mathrm{J/K}$)

Accepted Answer

$S = 7.3 	imes 10^{-22}\ \mathrm{J/K}$

Question 5

Which of the following best explains why the entropy of a perfect crystal at $0\ \mathrm{K}$ is zero?

Accepted Answer

There is only one possible microstate for the system.

Question 6

If a deck of cards is shuffled, how does the entropy compare to a deck in perfect order?

Accepted Answer

The shuffled deck has higher entropy due to more possible arrangements (microstates).

Question 7

Which of the following changes would increase the entropy of a system?

Accepted Answer

Heating a solid to melt it into a liquid.

Question 8

A system at $0\ \mathrm{K}$ is heated to $100\ \mathrm{K}$. What happens to the number of microstates $W$?

Accepted Answer

$W$ increases as the temperature increases.

Question 9

Which of the following is a real-world example of a system with only one microstate?

Accepted Answer

A perfect crystal at $0\ \mathrm{K}$.

Question 10

If the entropy of a system is $S = 2.76 	imes 10^{-22}\ \mathrm{J/K}$ and $k = 1.38 	imes 10^{-23}\ \mathrm{J/K}$, how many microstates does the system have?

Accepted Answer

$W = 10^{8}$

Question 11

Which of the following best describes the relationship between entropy and the number of microstates?

Accepted Answer

Entropy increases as the number of microstates increases.

Question 12

A chemical reaction produces more gas molecules than it consumes. What happens to the entropy of the system?

Accepted Answer

Entropy increases because there are more possible arrangements for the gas molecules.

Question 13

Which of the following would have the lowest entropy?

Accepted Answer

A perfect crystal at $0\ \mathrm{K}$.

Question 14

If $S = k \ln W$, what is the value of $W$ when $S = 0$?

Accepted Answer

$W = 1$

Question 15

Which of the following scenarios would result in the greatest increase in entropy?

Accepted Answer

Sublimation of dry ice (solid $\mathrm{CO}_2$) to gas.

Thermodynamics: Third Law and Entropy (Boltzmann Equation)

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