# Thermodynamic Work Relations

I was wondering if anyone knows where i can find the work relations for an ideal gas including isometric, isothermal, polytropic, isobaric, etc.

Q_Goest
Homework Helper
Gold Member
Hi blinder. I'm assuming you're looking for the equations to calculate the work done on an ideal gas when undergoing the various processes you've listed. A polytropic process is the most general, so we can start with that. Also, the equations should work just as well for compression or expansion (work in or out of the gas).

As you must already know PV^n = constant is a polytropic process. If you compress a gas, the work done is the integral of PdV. If we integrate that for a polytropic process you end up with:

W = (m R (T2 - T1) / (1-n) = (P2 V2 - P1 V1) / (1-n)
where m = mass
R = Gas Constant
T = temperature
n = polytropic exponent
P = absolute pressure
V = total volume
(for any value of n except 1)

For an isentropic compression, n = the ratio of specific heats of the gas (ex: 1.667 for a monotomic gas, 1.4 for a diatomic gas, etc...)

For an isobaric process, n = 0

For an isothermal process, n = 1 so you need to do the integration using n=1 which comes out to:

W = mRT ln (V2/V1) = mRT ln (P1/P2)

Hope that helps.