The work done in doubling the volume of $5$ moles of an ideal gas at a constant temperature of $500 \, K$ is ....... $J$.

When an ideal gas in a cylinder was compressed isothermally by a piston,the work done on the gas was found to be $1.5 \times 10^4 \ J$. During this process,about:

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is ${m_A}$ and that in $B$ is ${m_B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then:

$A$ 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.)

In an isothermal process,which statement is wrong?

The isothermal elasticity of a gas is equal to