During an adiabatic process, an ideal gas obeys the relation PV32= constant.  Calculate the final temperature of such a gas initially at a temperature T, if it is compressed adiabatically to half its initial volume.

PV32=constantPVγ=constant⇒γ=32Now, TVγ−1= constant where T is temperatureV is volume.i denotes initial condition of a systemf denotes final condition of a system.TiViγ−1=TfVfγ−1Tf=TiViVfγ−1=Ti(2)γ−1Tf=Ti(2)12−1=2TiTI=TTf=2T