Question

Thermodynamic cycle and the net energy transferred as heat?

Answer 1

Here's the problem:

A 2.00 mol diatomic gas initially at 300 K undergoes this cycle: It is (1) heated at a constant volume to 800 K, (2) then allowed to expand isothermally to its initial pressure, (3) then compressed at a constant pressure to its initial state. Assuming the gas molecules neither rotate nor oscillate, find (a) the net energy transferred as heat to the gas, (b) the net work done by the gas, and (c) the efficiency of the cycle.

I'm mostly concerned with the heat part of the problem. I have the question figured out and I got the right answers after some help, but I still don't completely understand why it was solved the way it was solved.

Here's what I did:



Q for constant volume: \[(5/2)(2.00)(8.31)(500)\]

Q for isothermal process: \[(2.00)(8.31)(800)\ln(\frac{ 8 }{ 3 })\]

Then, I added those together and that was the right answer. My questions are, why is it only these two processes that you add to find the net energy transferred as heat and why is the ratio for volume in the isothermal process the same as the ratio of the temperatures? How would you know to only add those two parts and how would you know to find the ratio like that? Any help would be appreciated.