Calculating work done on a gas- Adiabatic process PV diagram.

1. The problem statement, all variables and given/known data

As per attachment. Part iii

How would you do this question by integrating the work?

2. Relevant equations

W = – ∫P dV

PV^gamma = constant

3. The attempt at a solution

So I integrated the work with P= constant/ V^gamma and came up with this:

W = constant* ( Vf^(1-gamma)-Vi^(1-gamma) ) / (1-gamma)

So now how to I find the constant from the graph and information provided. This is what I was trying to do with not much luck:

constant = (Pi* Vi)^gamma / (Pf* Vf)^gamma

Am I missing something obvious?

Thanks in advance.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Attached Images
File Type: png 22.png (58.3 KB)

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