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## Homework Statement

A closed system consisting of 14.5 lb of air undergoes a polytropic process from p

_{1}= 80 lbf/in

^{2}, v

_{1}= 4 ft

^{3}/lb to a final state where p

_{2}= 20 lbf/in

^{2}, v

_{2}= 11 ft

^{3}/lb. Determine the amount of energy transfer by work, in Btu, for the process

## Homework Equations

W = ∫

_{v1}

^{v2}p dv = ∫

_{v1}

^{v2}c/v

^{n}dv

## The Attempt at a Solution

Using the relationship p

_{1}v

_{1}

^{n}= p

_{2}v

^{n}

_{2}

I solved for n with:

n = ln(p

_{2}/p

_{1})/ln(v

_{2}/v

_{1}) which gives me

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

W = p

_{2}v

_{2}- p

_{1}v

_{1}/(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?