One gm mol of a diatomic gas $(\gamma = 1.4)$ is compressed adiabatically so that its temperature rises from ${27^o}C$ to ${127^o}C$. The work done will be

A polyatomic gas $\left( {\gamma = \frac{4}{3}} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is ${P_o}$, its new pressure will be

Initial pressure and volume of a gas are $ P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $ V$. The final pressure of gas will 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

During the adiabatic expansion of $2 \,moles$ of a gas, the internal energy was found to have decreased by $100 J$. The work done by the gas in this process is ..... $J$

Air in a cylinder is suddenly compressed by a piston, which is then maintained at the same position. With the passage of time