$TV^{2/f} =$ constant
$\therefore \,\,\frac {2}{f}=\frac {2}{5}=x$





(Give $2^{1.2}=2.3 ; 2^{3.2}=9.2 ; R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P _0$ and $10 P _0$
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT _0$ and $19 RT _0$
$(3)$ The work $| W |$ done during the process is $13 RT _0$
$(4)$ Adiabatic constant of the gas mixture is $1.6$
