- #1
worryingchem
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Homework Statement
Methane at ## P_1 ## and ## T_1 ## is compressed to a pressure of ## P_2 ## adiabatically at steady-state. Calculate the work done on the compressor and the temperature ## T_2 ## of the discharge gas. Use ideal gas model.
Given:
## T_1, P_1, P_2, C_p, \gamma = 1.4 ##
## PV^\gamma = constant ##
## W = \int_{P_1}^{P_2} VdP ##
## \Delta H = \int_{T_1}^{T_2} C_p dT = W ##
Homework Equations
## dH = TdS + VdP ##
## dQ = TdS ##
Steady-state energy balance: ## \Delta H = W_{shaft} ##
The Attempt at a Solution
Hello,
my first question is that is this process reversible?
Because if I started from ## dH = TdS + VdP ##, in order to apply ## 0 = dQ = TdS ## to get ## dH = VdP ##, won't the process have to be reversible?
Then, using the energy balance, I make ## dH = VdP = dW ## and got the given equation ## W = \int_{P_1}^{P_2} VdP ##. My second question here is that can we use ## dW = -PdV ## here instead of ## dW = VdP ##? And why can't or can we? I'm confused as to when we can use ## dW = -PdV ##.
Thank you for your help.