# Determine the work and heat transfer

1. Feb 3, 2015

### Triathlete

1. The problem statement, all variables and given/known data

Steam in a piston-cylinder assembly undergoes a polytropic process. Kinetic and potential energy effects are negligible. For the process, determine the work and heat transfer, each in Btu per lb of steam.

p1 = 100 lbf/in2
p2 = 40 lbf/in2
v1 = 4.934 ft3/lb
v2 = 11.04 ft3/lb
u1 = 1136.2 Btu/lb
u2 = 1124.2 Btu/lb

2. Relevant equations

ΔE = Q - W

W = ∫v1v2pdV

3. The attempt at a solution

Since the process is polytropic, PVn = constant = p1V1n = p2V2n

Thus, W = ∫v1v2(constant/Vn)dV = (p2V2 - p1V1)/(1-n)

I used the relation p1V1n = p2V2n to find n, which gives me n = 1.14

Then, my plan is to plug the numbers into my integrated work function, but I am extremely confused on the units of this and I'm not really sure if I'm even working in the right direction. Basically I've gotten stuck at this point. Any help would be much appreciated.

2. Feb 4, 2015

### Staff: Mentor

Your equation for the work is correct. To get the work in BTU/lb, you need to first get it in ft-lbf/lb, and then convert the ft-lbf to BTU. Then you use the first law of thermo to get the heat, since you already know both W and ΔE.

Chet