An ideal gas expanding such that PT2=constant. The coefficient of volume expansion of the gas is

Let PT2= constant =k− PV=nRT⇒P2V2=n2R2T2⇒P3V2=n2R2K2  Both side differentiate, we get +3ΔPP=−2ΔVV  By equation (1), ΔPP+2ΔTT=0⇒ΔPP=−2ΔTT v=v0(1+γΔT)⇒ΔVV=γΔT  By equation (1), (2) and (3) We get, γ=3/T