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

During an adiabatic process, if the pressure of an ideal gas is propor

1.	During an adiabatic process, if the pressure of an ideal gas is proportional to the cube of its temperature, find gamma .
Answer» <P> Solution :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`