Let the initial volume of gas =V1 Gas is compressed adiabatically then the volume. V2=
V1
32
Initial temperature of gas =Ti (in kelvin) Final temperature of gas =αTi For diatomic gas, γ=
7
5
For adiabatic process, ⇒TVγ−1= constant When initial volume is V1, then adiabatic process is given as ⇒TiV1γ−1= constant .......(i) When volume is
1
32
of initial volume, then adiabatic process ∴αTi(
V1
32
)γ−1= constant .........(ii) Now, Eqs. (i) and (ii), we get or TiV1