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Calculating ideal gas compressor work and final temperature

  1. Oct 23, 2012 #1
    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.
     
  2. jcsd
  3. Oct 24, 2012 #2
    Cp=Cv+R

    γ=Cp/Cv

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

    Solve for T2

    Since adiabatic Q=0 therefore work=ΔU
     
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