In an adiabatic process where in pressure is increased by $\frac{2}{3}\% $ if $\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2},$ then the volume decreases by about

Given below are two statement 

Statement $-I$ : What $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( P _{1}, V _{1}, T _{1}\right)$ to state $\left( P _{2}, V _{2}, T _{2}\right)$, the work done is $W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }}$ and $R =$ universal gas constant,

Statement $-II$ : In the above case. when work is done on the gas. the temperature of the gas would rise.

Choose the correct answer from the options given below

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among $1,2,3$ and $4$ is

A motor-car tyre has a pressure of $2\, atm$ at $27\,^oC$. It suddenly burst's. If $\left( {\frac{{{C_p}}}{{{C_v}}}} \right) = 1.4$ for air, find the resulting temperatures (Given $4^{1/7} = 1.219$)

Two moles of an ideal monoatomic gas at ${27^o}C$ occupies a volume of $V.$ If the gas is expanded adiabatically to the volume $2V,$ then the work done by the gas will be ....... $J$ $[\gamma = 5/3,\,R = 8.31J/mol\,K]$

$5.6$ $liter$ of helium gas at $STP$ is adiabatically compressed to $0.7$ $liter$. Taking the initial temperature to be $T_1$, the work done in the process is