Question: [![Pressure - Volume diagram](https://i.stack.imgur.com/6JHKN.png)](https://i.stack.imgur.com/6JHKN.png)

Hi just came up to this question of how I should express the total heat taken in. I get that total work done by the gas is 5P0V0 (area of the polygon), and that Q\_net = W\_net should equal. But how do I find how much heat energy that has been absorbed by the system? Heat must be taken in and out (and the sum of input and output is what I understand as Q\_net).
I tried looking up on the internet, but it only provided steps on specific examples like isothermic, isobaric and so on. Is there a simple method for graphs like such?

The ultimate goal is to find the efficiency of the engine between temperatures a and b.

Answer: 
I will try to answer your question on heat absorbed and heat rejected thereby allowing you to calculate efficiency of the process.
1.)Split the question into 4 processes calculate work done and change in internal energy for each of the four.
2.)Use first law of thermodynamics to find Q in each process and when it comes out to be negative heat has been rejected and when it is positive heat is absorbed. Hence now you can use the formula for efficieny i.e $$\eta= 1-\dfrac{Q\_{\text{rejected}}}{Q\_{\text{absorbed}}}$$
The system has gone through a cycle, so the final state is the same as the initial state. That means that the change in internal energy is zero. Based on the 1st law of thermodynamics, what does that tell you about the relationship between the heat taken in and the amount of work done?