An ideal monoatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by the gas is $W_i$. If the process is adiabatic, the magnitude of work done by the gas is $W_a$. Which of the following is true?

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  …… $atm$

Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition 

Starting at temperature $300\; \mathrm{K},$ one mole of an ideal diatomic gas $(\gamma=1.4)$ is first compressed adiabatically from volume $\mathrm{V}_{1}$ to $\mathrm{V}_{2}=\frac{\mathrm{V}_{1}}{16} .$ It is then allowed to expand isobarically to volume $2 \mathrm{V}_{2} \cdot$ If all the processes are the quasi-static then the final temperature of the gas (in $\left. \mathrm{K}\right)$ is (to the nearest integer)

A tyre filled with air $({27^o}C,$ and $2$ atm) bursts, then what is temperature of air ……. $^oC$ $(\gamma = 1.5)$