Final answer:
The entropy change of a gas can be calculated using the equation ΔS = nC_p ln(T_f/T_i). In certain examples, the change in entropy of the universe can be determined by considering the change in entropy of the system and the surroundings. In other examples, the change in entropy of the universe is equal to the sum of the change in entropy of different components.
Step-by-step explanation:
The entropy change of a gas can be calculated using the equation ΔS = nC_p ln(T_f/T_i), where ΔS is the change in entropy, n is the number of moles of the gas, C_p is the molar heat capacity at constant pressure, T_f is the final temperature, and T_i is the initial temperature.
In Example 4.8, the entropy change of the universe can be determined by considering the change in entropy of the gas and the surroundings. When the gas expands into the larger volume, it can be seen as a decrease in order and an increase in entropy. The surroundings, being thermally insulating, experience no change in entropy.
In Example 4.7, the change in entropy of the ice and the universe can be found by considering the flow of heat from the reservoir to the ice as it melts. The change in entropy of the universe is equal to the sum of the change in entropy of the ice and the change in entropy of the reservoir.