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HethensEnd25
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Homework Statement
One mole of an ideal gas is reversibly compressed from 1 bar to P2
bar that results in temperature increase from 400 K to 950 K. Calculate the heat
transferred during the process and the final pressure, if the path followed by the gas can
be given by PV1.55 = , and the molar heat capacity of the gas is given by
Cp/R = 3.85 + 0.57×10-3T (where T is in K)
Homework Equations
dU=dQ+dW
The Attempt at a Solution
my attempt at a solution.
1. I used the first law of thermodynamics to get
dU=dQ+dW
solving for dQ
dQ=dU-dW ===> dQ=CvdT+PdV
2. Using Ideal gas solved for T then differentiated
RdT=PdV +VdP
3. It was given that PV1.55=Constant
I know since it is a real number I can use steps of a polytropic process
PVδ=Constant
This is where I am getting hung up. My books steps to solution say that using
RdT=PdV +VdP solving for PdV
is the next step to solve the above expression PVδ=Constant.
It then says that PδVδ-1dV=-VδdP from which VdP=-PδdV
My question is how did they derive that expression from the PVδ=Constant
the end result being that
PdV=RdT/(1-δ)
Any and all help clarifying this for me would be greatly appreciated I have other formula that are all plug and chug but I would rather understand the steps involved in solving the problem with these constants.
Best Regards,
D
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