Determine the amount of energy transfer by work in btu

[Northbysouth]

Homework Statement

A closed system consisting of 14.5 lb of air undergoes a polytropic process from p₁ = 80 lbf/in², v₁ = 4 ft³/lb to a final state where p₂= 20 lbf/in², v₂ = 11 ft³/lb. Determine the amount of energy transfer by work, in Btu, for the process

Homework Equations

W = ∫_v1^v2p dv = ∫_v1^v2 c/vⁿ dv

The Attempt at a Solution

Using the relationship p₁v₁ⁿ = p₂vⁿ₂

I solved for n with:

n = ln(p₂/p₁)/ln(v₂/v₁) which gives me

n = -1.3704 but other people I've spoken to have gotten +1.3704 which, when used in:

W = p₂v₂ - p₁v₁/(1-n)

gives me 563714.9 lbf-ft, which then gives me 725 Btu when converted to Btu.

Why do I get -1.3704 instead of a positive?

 

[rude man]

You did not solve for n correctly. It's
n = ln(p1/p2)/ln(V1/V2) > 0.