# Thermodynamics exercise.

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

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Hello TSny, thx 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) P1-γ Tγ=const. What do you think?
The statement doesn't specify if the process is reversible actually...

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