Calculating ideal gas compressor work and final temperature

[supahtofu]

A compressor is being used to adiabatically pressurize three moles of ideal gas from 5 bar and 150 C to 50 bar. Determine the minimum work that must be supplied to the compressor and the outlet temperature of the ideal gas. Assume the ideal gas has a constant pressure heat capacity of 29 J/(mol*K).

Relevant equations: steady state energy balance: 0=Mk(deltaH)+Q+W
Cp=deltaH/deltaT

Attempt at solution: The only problem I'm having is determining how to find T2. With T2 I can solve for delta H and plug it into the energy balance to find W, but I have no clue how to get T2. I don't think I can do anything with the ideal gas law either so I'm not sure what to do. I was thinking maybe P1/T1=P2/T2 but I don't believe the conditions are quite right for that, pllus we've never used that equation in class. Anyone have any ideas or advice?

Thank you for your time.

 

[RTW69]

C_p=C_v+R

γ=C_p/C_v

For adiabatic Processes:
T₂/T₁=(P₂/P₁)^((γ-1)/γ)

Solve for T₂

Since adiabatic Q=0 therefore work=ΔU