- #1

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I'm really confused with this and would appreciate any help.

## Homework Statement

a) Show that the work done on a gas during a quasistatic adiabatic compression is given by:

[tex]W = \frac{P_f V_f - P_i V_i}{\gamma - 1}[/tex]

b) Show that the work done by a gas during a quasistatic adiabatic compression is given by:

[tex]w = \frac{P_i V_i - P_f V_f}{\gamma - 1}[/tex]

## Homework Equations

[tex]w = -W[/tex]

[tex]PV^{\gamma} = K[/tex]

## The Attempt at a Solution

a) [tex]dW = -PdV[/tex]

[tex]P = KV^{- \gamma}[/tex]

[tex]W = -K \left[\frac{V^{1- \gamma}}{1 - \gamma} \right]^{V_f} _{V_i}[/tex]

[tex]W = - \frac{P_f V_f - P_i V_i}{1 - \gamma}[/tex]

[tex]W = \frac{P_i V_i - P_f V_f}{\gamma - 1}[/tex]

I don't understand where I've gone wrong.

b) [tex]w = -W[/tex]

[tex]w = - \frac{P_i V_i - P_f V_f}{\gamma - 1}[/tex]

[tex]w = \frac{P_f V_f - P_i V_i}{1 - \gamma}[/tex]

I also get this answer if I derive w from:

[tex]dw = PdV[/tex]

I've probably got a minus sign mixed up, or something like that, but I've been through the derivation so many times it's invading my dreams. Okay, maybe it isn't that bad, but I'm really struggling.