# Thermodynamics problem

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

ehild
Homework Helper
thenewbosco said:
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

Replace back $$V^{\gamma}$$ by constant/P.

ehild