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
W = ∫v1v2p dv = ∫v1v2 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?