The P-V relation for monoatomic ideal gas undergoing an adiabatic change is

short cut    PVγ=CONSTANTALTERNATE METHOD: We know that E=32NkT        or      dE=32NkdTFurther, dW=P⋅dV=NkTV⋅dVFor Adiabatic change dE = - dW. Hence32NkdT=−NkTV⋅dVor     dTT=−23dVV     or    dTT+23dVV=0∴ log⁡T+23log⁡V= constant or    TV2/3= constant or     PV5/3= constant (Using ideal gas law)