Gas Cycle Process; Adiabatic, Isovolumetric and Isothermal

[RCulling]

Homework Statement

A monatomic gas has V1 P1 and T1 (volume pressure and temp) at state 1
The gas then goes through the following process

adiabatic expansion to stage 2 (exapands to twice its volume)
isovolumetric heating so it gets back to T1; stage 3
isothermal compression back to intial state

Homework Equations

- Sketch on pV diagram? (done this)
- derive expressions for P2 and P3 (in terms of p1 and $$\gamma$$) ?
- derive expressions for T2 and T3 (in terms of T1 and $$\gamma$$)?
- expression for net work done in 1 cycle?
- is this an engine or refridgerator?

The Attempt at a Solution

i've managed to find

P2 = P1 / (2^$$\gamma$$)
and that $$\gamma$$ = 5/3

The 2 questions in bold are the ones really stressing me out; if someone could please put up some solutions or just point me in the right way that would be great :)
Thanks

 

[kuruman]

Can you find p₃ in terms of p₁? What is the equation for an isotherm? Use it the same way you used the adiabatic equation to find the relation between the two pressures. Once you have p₂ and p₃ in terms of p¹, use the ideal gas Law to get the temperatures.

 

[RCulling]

The isotherm eqn; W = nRT*ln(vi/vf)
where vi = v1 and vf = v3?

 

[kuruman]

That's the work for an isothermal process. How about p₁V₁=p₃V₃? A straightforward result of the ideal gas law.

 

[RCulling]

Ah ofcourse :| .. Sounds like me to over think the simple(correct) answer

Thank you :)
- i'll post on here if i can't figure the rest