Question

10 L of a gas at 5.0 atm pressure at 25°C goes through the following expansion, compression steps while in an insulated container which cannot gain or lose heat.

1) Pressure is dropped to 2.0 atm.
2) Gas expands to 25 L.
3) Pressure is increased to 5.0 atm.
4) Gas is compressed back to 10 L.

Which of the following statements is true about the process?
A) The final temperature of the gas will be greater than 25°C because more work was done by the system in expanding the gas than was done on the system in compressing the gas.
B) The final temperature of the gas will be greater than 25°C because more work was done on they system in compressing the gas than was done by the system in expanding the gas.
C) The final temperature of the gas will be lower than 25°C because more work was done by the system in expanding the gas than was done on the system in compressing the gas.
D) The final temperature of the gas will be lower than 25°C because more work was done on they system in compressing the gas than was done by the system in expanding the gas.
E) The final temperature of the gas will be 25°C because the gas is returned to the same pressure and volume.

Answer 1

The final temperature of the gas will be lower than 25°C because more work was done on the system in compressing the gas than was done by the system in expanding the gas.

Step-by-step explanation:

The final temperature of the gas will not be 25°C because the pressure and volume of the gas have changed during the expansion and compression.

In an adiabatic process, when a gas expands, it does work on its surroundings and its temperature decreases. When a gas is compressed, work is done on it and its temperature increases. Therefore, in this case, more work is done by the system in compressing the gas than is done by the system in expanding the gas. As a result, the final temperature of the gas will be lower than 25°C.