Compare burning of fuel to reversible supply of heat

In summary: C_v$ is the specific heat capacity at constant volume, $T$ is the temperature, $P$ is the pressure and $V$ is the volume. Using the ideal gas law, $PV=nRT$, and the definition of $C_p$ and $C_v$, we can derive the expression $TP^E=constant$, where $E=(1-X)/X$ and $X=C_p/C_v$. This expression holds for reversible adiabatic processes, where there is no heat transfer and the gas behaves in an ideal manner.
  • #1
trelek2
88
0
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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  • #2
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: $$dU=C_vdT=-PdV$$
 

1. How does the burning of fuel compare to the reversible supply of heat?

The burning of fuel and the reversible supply of heat are two different processes that involve the transfer of energy. Burning of fuel is a one-way process that produces heat through the chemical reaction of a fuel source, while the reversible supply of heat is a cyclical process where heat is absorbed and released repeatedly.

2. Which process is more efficient in terms of energy production?

The reversible supply of heat is more efficient in terms of energy production. This is because it utilizes a cyclical process, meaning that the heat energy is not lost but rather recycled and reused. On the other hand, burning of fuel is a one-time process that results in the loss of some energy in the form of waste heat.

3. How do these processes affect the environment?

Burning of fuel is known to have a negative impact on the environment as it releases harmful gases and pollutants into the atmosphere. On the other hand, the reversible supply of heat is a more environmentally friendly process as it does not produce any emissions or pollutants.

4. Which process is more cost-effective?

In terms of cost, the reversible supply of heat is more cost-effective in the long run. While the initial cost of setting up a system for reversible heat supply may be higher, the cyclical nature of the process means that it can save money on fuel costs in the long term. Burning of fuel, on the other hand, requires a constant supply of fuel which can be costly.

5. Are there any industries or applications that use the reversible supply of heat?

Yes, there are several industries and applications that use reversible supply of heat. Some examples include geothermal power plants, refrigeration systems, and air conditioning systems. These industries and applications utilize the reversible supply of heat to efficiently transfer and manage heat energy.

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