# Show that the work done in thermo

1. Oct 23, 2005

### thenewbosco

hello the problem is as stated:
a cylinder containing n moles of an ideal gas undergoes an adiabatic process. using $$W=-\int Pdv$$ and using the condition $$PV^\gamma=constant$$, show that the work done is:
$$W=(\frac{1}{\gamma - 1}(PfVf - PiVi)$$ where Pf is final pressure, Pi is initial pressure...
I tried substituting that $$P=\frac{constant}{V^\gamma}$$ into the integral, and evaluating from Vi to Vf, but this still leaves the gamma as an exponent. how can i go about solving this one?
thanks

2. Oct 23, 2005

### Gokul43201

Staff Emeritus
Right, you have an exponential term that looks like $V^{1- \gamma}$. Write this as a product of two terms, one of which is V itself. What can you do with the other part ?

3. Oct 24, 2005

### thenewbosco

awesome thanks for your help. all i needed was to see it as 1-gamma, instead of how i had it as -gamma +1. it made a lot of difference.