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

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SUMMARY

The discussion revolves around calculating the gas pressure in state 3 of a thermodynamic cycle involving an ideal diatomic gas with a specific heat ratio (γ) of 1.40 and an efficiency (φ) of 0.40. The cycle consists of four processes, with constant pressure processes occurring between states 1 to 2 and 3 to 4, while the other two processes are adiabatic. The lowest pressure in the cycle is established at 1 atm in state 1, and the relationship between pressure and temperature during adiabatic processes is defined by the formula P1/γ T^γ = constant, which is applicable under the assumption of reversibility.

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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.
 
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OK for part (a). For part (b), think of a way to relate T and P for the adiabatic processes.
 
Last edited:
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) P1-γ Tγ=const. What do you think?
The statement doesn't specify if the process is reversible actually...
 
Yes, that's the correct formula. For these types of questions you can generally assume that the entire cycle is reversible.
 

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