Work done in a reversible adiabatic expansion

In summary, the conversation discusses determining the work done of a reversible adiabatic expansion. The system is adiabatic, so Q=0 and ΔU=Wrev. However, because both pressure and volume change, the formula W=pexΔV cannot be used. The variables Cv, Cp, Ti, Tf, Pi, Pf, Vi, and Vf are known, but finding the right formula proves to be a challenge. It is mentioned that one state variable remains constant, and the formula ΔU=CvΔT=(Cp-R)ΔT always holds for an ideal gas.
  • #1
Trowa
6
0
Hi there!

I have to determine the work done of a reversible adiabatic expansion. Becauce the system is adiabatic: Q = 0 so [tex]\Delta[/tex]U = Wrev

Becauce both the pressure and the volume changes I can't use W = pex[tex]\Delta[/tex]V.

Homework Statement


Cv, Cp, Ti, Tf, Pi, Pf, Vi, Vf are known

The Attempt at a Solution



I thought at first that I could use [tex]\Delta[/tex]U = CV.[tex]\Delta[/tex]T but the volume is not constant so I don't know if I could use it.

Who can help me find the right formula?

Thanx in Advance!
 
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  • #2
Hi Trowa, welcome to PF.

(1) Because no heat goes in or out of the system, and because the process is reversible, one state variable remains constant. It's one that you haven't listed. What is it?

(2) [itex]\Delta U =c_V\Delta T=(c_P-R)\Delta T[/itex] always holds for an ideal gas, and doesn't require constant volume, constant pressure, or any other condition.
 
  • #3
Thanx for the fast response.
:smile:
 

1. What is a reversible adiabatic expansion?

A reversible adiabatic expansion is a process in thermodynamics where a gas expands without any exchange of heat with its surroundings. This means that the expansion is carried out in a perfectly insulated system where no energy is lost or gained in the form of heat.

2. How is work done in a reversible adiabatic expansion?

In a reversible adiabatic expansion, work is done when the gas expands against a constant external pressure. This work is equal to the negative of the change in internal energy of the gas, as described by the first law of thermodynamics.

3. What is the equation for work done in a reversible adiabatic expansion?

The equation for work done in a reversible adiabatic expansion is W = -nCv(Tf-Ti), where W is the work done, n is the number of moles of gas, Cv is the molar specific heat at constant volume, Tf is the final temperature, and Ti is the initial temperature.

4. How is reversible adiabatic expansion different from irreversible adiabatic expansion?

In a reversible adiabatic expansion, the process is carried out slowly and the system remains in thermodynamic equilibrium throughout the expansion. This allows for the gas to always be at a temperature slightly lower than the external temperature, resulting in a more efficient expansion. In an irreversible adiabatic expansion, the process is carried out quickly and the system is not in equilibrium, resulting in a higher final temperature and less efficient expansion.

5. What are some real-life applications of reversible adiabatic expansion?

Reversible adiabatic expansion is used in various industrial processes, such as in gas turbines, where it is used to produce work and generate electricity. It is also used in refrigeration systems, where the gas is compressed and then allowed to expand adiabatically, resulting in a decrease in temperature and allowing for cooling. Reversible adiabatic expansion is also used in the production of compressed air and in the expansion of gases in fuel cells.

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