What is the gas pressure in state 3 if the efficiency is 0.40?

[itsjorge]

Homework Statement

An engine works with an ideal diatomic gas (γ=1.40) according to a thermodynamic cycle consisting in four
processes that take the gas successively through the states 1, 2, 3 and 4. The processes 1 -> 2 and 3 -> 4 take
place at constant pressure and the two other processes are adiabatic. The cycle’s lowest pressure is 1 atm and
corresponds to the state 1.
a. Find an expression for the cycle’s efficiency exclusively in terms of the temperatures of the states 1,
2, 3 and 4.
b. If the efficiency is φ=0.40, what is the gas pressure in state 3?

2. The attempt at a solution

Ok, first part is easy (I guess) here's what I did http://imgur.com/hpBxIex if someone could give it a look I'd be very thankful. I'm sorry I cannot give you the P-V diagram because I don't know how to draw in this PC.
The second part is where it gets tougher because I only have 2 pieces of information and I really cannot relate them. If someone could sketch the solution I'd be very thankful.

 

[TSny]

OK for part (a). For part (b), think of a way to relate T and P for the adiabatic processes.

 

[itsjorge]

Hello TSny, thanks for replying, thing is my professor didn't give us a way to relate P and T however I found this formula in wikipedia but I'm not sure if it's correct: (It's valid iff the process is reversible) P^1-γ T^γ=const. What do you think?
The statement doesn't specify if the process is reversible actually...

 

[TSny]

Yes, that's the correct formula. For these types of questions you can generally assume that the entire cycle is reversible.