How to Calculate Net Heat Transfer in an Isochoric Process

[James.1809]

Hi, I'm really struggling with a thermodynamics coursework question, I'm not looking for the answer straight up, just wondering how to go about solving the problem as it's been racking my brain for a stupid amount of time. Here's the problem I've been given:

Shaft work (500kJ/kg) is transferred to an air-filled frictionless piston-cylinder device. Determine the net heat transfer (kJ/kg) if the initial state of the air is T1=200C, P1=400kPa and the final state of the air is T2=250C.

See the attachment for a diagram of the cylinder in question. I'm not sure whether to assume if the process is isochoric and if so, the internal energy's equal to the heat transferred, but to work that out I need to know the specific heat capacity of the air. It's got me stumped!

Any help is greatly appreciated!

 

[Valkarie]

The first thing you need to do is to identify the process. Since there is no mention of a change in volume, it is likely that the process is isobaric (constant pressure). This means that the work done on the air is equal to the change in internal energy, i.e. W = ΔU. Since the initial and final temperatures are given, you can calculate the change in internal energy using the ideal gas equation of state: ΔU = mCv(T2-T1) where m is the mass of the air, Cv is the specific heat capacity at constant volume and T2 and T1 are the final and initial temperatures, respectively. Once you have calculated the change in internal energy, you can then calculate the net heat transfer by subtracting the shaft work from the change in internal energy: Qnet = ΔU - W Hope this helps!