Compare burning of fuel to reversible supply of heat

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SUMMARY

The discussion centers on the thermodynamic principles governing jet engines, specifically the comparison between the irreversible process of fuel combustion and the reversible supply of heat. The user seeks clarification on why calculations for heating air at constant pressure in a jet engine can be treated as reversible. Additionally, the user inquires about the derivation of the expression for reversible adiabatic processes, represented as TP^E=constant, where E=(1-X)/X and X= Cp/Cv. The response indicates that this expression arises from the first law of thermodynamics applied to reversible adiabatic expansion of an ideal gas.

PREREQUISITES
  • Understanding of thermodynamics, specifically the first law of thermodynamics.
  • Familiarity with ideal gas laws and properties.
  • Knowledge of specific heat capacities (Cp and Cv) and their significance in thermodynamic processes.
  • Basic principles of reversible and irreversible processes in thermodynamics.
NEXT STEPS
  • Study the derivation of the first law of thermodynamics in the context of adiabatic processes.
  • Research the concept of reversible processes in thermodynamics and their applications.
  • Explore the implications of Cp and Cv in real-world applications, particularly in jet engine design.
  • Learn about the ideal gas law and its applications in thermodynamic calculations.
USEFUL FOR

Engineers, thermodynamics students, and professionals involved in aerospace engineering or jet engine design will benefit from this discussion, particularly those looking to deepen their understanding of heat transfer and thermodynamic processes.

trelek2
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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.
 
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trelek2 said:
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: $$dU=C_vdT=-PdV$$
 

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