In adiabatic processes no heat transfer occurs. This means that in the equation that We can also use the fact that for any process for an ideal gas, adiabatic or not, internal energy changes are given by(1) and the work done by the gas is given by

Using these, the equationbecomes

Since we are assuming the gas is ideal we can useasobtaining

We can separate vaiables to obtainand integrate:

(2)

Nowso (2) becomes(3)

Substituteinto (3) to obtain

We can find the work done by an gas during an adiabatic process usingand (1) to obtain

Use ofthen gives