Compare burning of fuel to reversible supply of heat

[trelek2]

Hi!

I'm working on a problem regarding a jet engine and I actually did solve it but I'm not sure about two things:

At some point in the engine, air is heated at constant pressure (with the gas being almost stationary). Of course, this is done by the burning of fuel. But I found the information that in order to carry out the calculation I must proceed as if heat was supplied reversibly.
Why is the process of burning of fuel, which is clearly not reversible, the same as if the heat was supplied reversibly?

Secend question: I used the following expression (relating the temperature and pressure of an ideal gas) for the reversible adiabatic expansion/compression of gas:
TP^E=constant where E=(1-X)/X, where X= Cp/Cv. Note here that E and X are meaningless, but Cp,Cv are the specific heat capacities at constant pressure and costant volume.
My question is: Where does this expression come from and what is the formal proof for it. If anyone knows a link to a site with an explanation of this, please share it with me, I will be very grateful.

 

[Chestermiller]

Hi!

I'm working on a problem regarding a jet engine and I actually did solve it but I'm not sure about two things:

At some point in the engine, air is heated at constant pressure (with the gas being almost stationary). Of course, this is done by the burning of fuel. But I found the information that in order to carry out the calculation I must proceed as if heat was supplied reversibly.
Why is the process of burning of fuel, which is clearly not reversible, the same as if the heat was supplied reversibly?

Secend question: I used the following expression (relating the temperature and pressure of an ideal gas) for the reversible adiabatic expansion/compression of gas:
TP^E=constant where E=(1-X)/X, where X= Cp/Cv. Note here that E and X are meaningless, but Cp,Cv are the specific heat capacities at constant pressure and costant volume.
My question is: Where does this expression come from and what is the formal proof for it. If anyone knows a link to a site with an explanation of this, please share it with me, I will be very grateful.

It comes from solving the 1st law equation for reversible adiabatic expansion of an ideal gas: $$dU=C_vdT=-PdV$$