Adiabatic Process: Cv (Molar Heat)

[C_Ovidiu]

Say we have a cilinder, thermally isolated from the environment, divided in two parts by a piston. In the left part we have an ideal gas, in the right part an unstretched spring. After we set free the piston, in the final phase, we fin that the gas' volume has doubled, while it's temperature is 10/11 the initial temperature. Find Cv (molar heat).

If we consider $$L=-\Delta U$$ that we find a reasonable result. However, since the process is adibatic(that is why I used equation above) if we try to aply the formula $$T\cdot V^{\gamma-1}=ct$$ we find a totally different result. Why is that ?

 

[Redbelly98]

Since nobody else has responded, I'll take a stab at it.

Using T V ^γ-1=constant should give the right answer.

Is L supposed to be work done by the piston? How did you use that to calculate γ?

What did you get for γ using the two methods?

 

[wywong]

The formula for adiabatic expansion only applies in quasi-static situations. In your situation, the spring provides no force initially, so it is definitely not quasi-static. Only the conservation of energy equation applies.