During an adiabatic process, if the pressure of an ideal gas is proportional to the cube of its temperature, find `gamma` .

Explanation

For an ideal gas of one mole `PV=RT^(3)`
During an adiabatic process `P oo T^(3) rArr P=KT^(3)`
`P=K((PV)/(R ))^(3)rArr P=((K)/(R^(3)))P^(3)V^(3)`
`P^(2)V^(3)=` constant`" "PV^(3//2)=` constant
Comparing it with the equation
`PV^(gamma) =` constant for an adiabatic process,
we get `gamma=3//2`