How to calculate the efficiency from a p-v diagram (thermodynamics)

Discussion in 'Physics' started by Nathan Lowe, Oct 8, 2018.

1. Nathan LoweGuest

Question: Calculate the efficiency of the real and ideal cycles.

The process 1-2 is polytropic, 2-3 is isochoric, 3-4 is polytropic as well, and 4-1 completes the cycle with another isochoric process.

My attempt: I know that to calculate the efficiency of a cycle we must know the work done as output and the heat supplied to the system. As such, the efficiency will be the ratio of these two: $$\eta = \frac{w_{out}}{q_{in}}$$ From this diagram, I am able to calculate $w_{out}$ but I don't see how $q_{in}$ can be determined.

I originally just thought it to be equal to the work done from process 1-2, but I don't see think that is correct at all.

Would the heat in be through the isochoric process 4-1?

I'm not even sure if the heat in can be calculated straight from the p-v diagram.

Any help regarding how to determine $q_{in}$ would be greatly appreciated.

Edit: Can assume a working substance is undergoing this cycle. E.g. air