Lesson: Energy Changes in Gas Expansions

In this lesson, we will learn how to classify gas expansion and compression processes based on changes in heat, entropy, enthalpy, or internal energy.

Worksheet: 12 Questions

Q1:

Consider 0.1 mol of an ideal gas contained in a cylinder of volume 2.5 dm3 at a pressure of 1 bar and a temperature of 301 K. Next, suppose you consider three different processes for changing the state of the gas sample to one in which the volume is reduced to 0.25 dm3, the pressure is increased to 10 bar, and the temperature is 301 K (the same as the temperature in the initial state). The paths of the three alternative processes are specified as follows.

Process 1 is a two-step process in which the gas sample is first heated at constant volume until the pressure reaches a value of 10 bar, and then the gas is cooled under constant pressure (10 bar) until its equilibrium volume is reduced to 0.25 dm3 and its temperature is 301 K.

Process 2 is a two-step process in which the gas sample is first cooled under constant pressure (1 bar) until its equilibrium volume is reduced to 0.25 dm3, and then the gas is heated under constant volume conditions until its pressure reaches a value of 10 bar and its temperature is 301 K.

Process 3 is a single-step process in which the gas is isothermally compressed from its initial state to its final state at a fixed temperature of 301 K.

Which of the three processes above would require the least amount of work in effecting the specified change of state, and what would be the Δ𝑈 (change in internal energy) for this process?

Q2:

Consider a process in which a gas is expanded adiabatically and reversibly under constant-pressure conditions, and the amount of work done by the gas in this process is 10 kJ. What changes in the internal energy (𝑈) and entropy (𝑆) of the gas will accompany this process?

Q3:

Consider a process in which a 2 mol sample of a certain gas is heated reversibly from 275 K to 375 K under a constant pressure of 1 bar, and the entropy change for the gas is Δ𝑆=13.3/JK. What will the value of Δ𝑆 for a process in which the same gas sample is heated irreversibly from 275 K to 375 K under a fixed pressure of 1 bar?

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