Steam, Piston-cylinder system polytropic

[Ready2GoXtr]

Homework Statement

Steam in a piston-cylinder assembly undergoes a polytropic process, with n = 2. The initial state is p1 = 500lbf/in^2, v1 = 1.701 ft^3/lbm and u1 = 1363.3 BTU/lbm. IN the final state, u2 = 990,58 BTU/lbm. During the process, there is heat transfer from the steam of magnitude 342.9 BTU. THe mass of the steam is 1.2 lbm. Neglecting changes in kinetic and potential energies, calculate the work of the process, in BTU, and the final specific volume in ft^3/lbm.

Homework Equations

W=Q-dU

The Attempt at a Solution

So far all I can do is answer the first part of the question:
W = -342.9 BTU - m(u2-u1)
W = 104.4

 

[Q_Goest]

Hi Ready. This looks a bit tricky. I don't know of any way to directly calculate this. The only way I can do this is to pull values from the steam tables such that they match the requirements for final internal energy and polytropic exponent. When I do that, I can find the final state. Note that the final state will be saturated (ie: a mixture of saturated gas and liquid).

VOF = 0.853, P=100 psia, T=327.7 F

 

[Redbelly98]

I'm wondering if we can take the first sentence at face value, that PV² is constant? And not worry about whether there is a mixture of liquid and vapor ...

EDIT:
Q_Goest, shouldn't the volume increase? It may not condense into liquid after all.

 

[Redbelly98]

Okay, I've got a solution that says the steam does not condense (checked it with a steam table).

Hint: what does U tell us about the product P*V? Use that, and the P*V² relation, to get a solution for P_final and V_final.

EDIT:

I'll have to retract this suggestion. I was thinking that P*V/U should be a constant, but we can't simply assume that for a real gas.

Q_Goest's suggestion to use steam tables looks like the right approach.