An ideal gas at a pressures of $1$ atmosphere and temperature of ${27^o}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure, then the final temperature is ….. $^oC$ ($\gamma  = 3/2$)

What is an adiabatic process ? Derive an expression for work done in an adiabatic process.

Match List$-I$ with List$-II$

Choose the correct answer from the options given below

A mass of diatomic gas $(\gamma = 1 .4)$ at a pressure of $2$ atmospheres is compressed adiabatically so that its temperature rises from $27^o C$ to $927^o C.$ The pressure of the gas in the final state is  …… $atm$

A mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure $P _0$, volume $V _0$ and temperature $T _0$. If the gas mixture is adiabatically compressed to a volume $V _0 / 4$, then the correct statement(s) is/are,

(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 $1.6$