Determine the work and heat transfer

[Triathlete]

Homework Statement

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

Homework Equations

ΔE = Q - W

W = ∫_v1^v2pdV

The Attempt at a Solution

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

Thus, W = ∫_v1^v2(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.

 

[Chestermiller]

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