When heat is given to a gas in an isothermal change,the result will be

One mole of ${O_2}$ gas having a volume equal to $22.4 \text{ litres}$ at $0^{\circ}C$ and $1 \text{ atmospheric pressure}$ is compressed isothermally so that its volume reduces to $11.2 \text{ litres}$. The work done in this process is ...... $J$.

$A$ piston of mass $M$ is hung from a massless spring whose restoring force law is given by $F = -kx^3$,where $k$ is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts,where the bottom part is filled with $n$ moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature $T$) with the help of a heating filament (with negligible volume) mounted in the lower part of the chamber,so that the piston moves up from a height $L_0$ to $L_1$. Calculate the total energy delivered by the filament. (Assume the spring to be in its natural length before heating.)

During an isothermal expansion of an ideal gas,

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$, respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$, respectively. Then

In an isothermal reversible expansion,if the volume of $96\, g$ of oxygen at $27^{\circ}C$ is increased from $70\, L$ to $140\, L$,then the work done by the gas will be