The pressure and density of a diatomic gas $\gamma  = 7/5$ change adiabatically from $(P, d)$ to $(P', d').$ If $\frac{{d'}}{d} = 32,$ then $\frac{{P'}}{P}$should be

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

One mole of an ideal monoatomic gas undergoes the following four reversible processes:

Step $1$ It is first compressed adiabatically from volume $8.0 \,m ^{3}$ to $1.0 \,m ^{3}$.

Step $2$ Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \,m ^{3}$.

Step $3$ Then expanded adiabatically to volume $80.0 \,m ^{3}$.

Step $4$ Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \,m ^{3}$.

Then, $T_{1} / T_{2}$ is

Which is the correct statement

Write the expression of work for an ideal gas in isobaric process.

The work of $146\ kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^o  C$. The gas is $(R=8.3\ J\ mol^{-1} K^{-1})$