Cylinder Assembly
June 19th, 2004
Thermodynamics Question involving a piston-cylinder assembly?
Full Question:
A gas contained within a piston‐cylinder assembly undergoes two processes, A and B, between the same end states, 1 and 2, where p1 = 10 bar, V1 = 0.1m3, U1=400kJ and p2= 1 bar, V2=1.0 m3, U2=200 kJ:
Process A: Process from 1 to 2 during which the pressure‐volume relation is pV= constant
Process B: Constant‐volume from state 1 to a pressure of 2 bar, followed by a linear‐volume process to state2.
Kinetic and potential energy can be ignored. For each of processes A and B, (a) sketch the process on p‐V coordinates, (b) evaluate the work in kJ, and (c) evaluate the heat transfer, in kJ.
I have already finished the question for ProcessA and I am working on Process B. My question is, wouldn’t the values of Work and Heat Transfer be the same as process A because the intial and final conditions are the same. Wouldn’t the only thing that changes would be the process sketch.
No, the heat and work will not be the same for process B as they were in process A. Heat and work are PATH variables and so if the process follows a different path then the values of heat and work are different. The change in state variables, like U, must be the same for paths a and b because they begin and end in the same state.
Here I will call the two steps in path B: B1 and B2. The work in B1 is zero since the volume is constant (assuming that only moving boundary work crosses the system boundary).
For step B2, the work is the area under a straight line from {P1,V1} to P2,{V2} = [(P2+P1)/2]*(V2-V1)=495kJ (done by the system on the surroundings). So, the total boundary work for path B is 495 kJ.
You can then determine Q from the 1st Law: Q-W=deltaU. So, Q = deltaU+W = U2-U1+W = 200-400+495=295kJ.
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