How is Work Done in an Adiabatic Process of an Ideal Gas Calculated?

[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

 

[Gokul43201]

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 ?

 

[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.