Question about Heat Capacity for Problem 9.13

[Curtis Tam 1J]

During the test of an internal combustion engine, 3.00L of nitrogen gas at 18.5C was compressed suddenly (and irreversibly) to 0.500L by driving in a piston. In the process, the temperature of the gas increased to 28.1C. Assume ideal behavior. What is the change in entropy of the gas.

The solution was already corrected on the course website under Errors in the Solution Manual but I still don't get why the answer uses the heat capacity of nitrogen at constant volume for calculating the entropy change due to temperature change. If it uses Cv, doesn't that imply that there was no volume change when there is one described in the problem. In other words, how come we wouldn't use the heat capacity at constant pressure, which is 7/2R?

Thanks!

[Alyssa Pelak 1J]

You use Cv when calculating the temperature change because you are ignoring the change in volume for that part. So, in this question you are calculating the total change in entropy by calculating temperature change and volume change independent of one another. Therefore, when you change volume you can use a constant temperature and when you calculate temperature change you can use a constant volume. You can do this because entropy is a state function allowing you to calculate each independent of each other and add them together.

I asked a UA when we used constant pressure and they said that essentially we use constant pressure only when its explicit stated in the problem.