Starting with the same initial conditions, an ideal gas expands from volume $V_{1}$ to $V_{2}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal. $W _{2}$. if the process is purely adiabatic and $W _{3}$ if the process is purely isobaric. Then, choose the coned option

When a gas expands adiabatically

The work done in which of the following processes is equal to the internal energy of the system?

A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is

Helium at ${27^o}C$ has a volume of $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be ....... $^oC$ $[\gamma = 5/3]$

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