The change in the entropy of $1$ mole of an ideal gas which undergoes an isothermal process from an initial state $(P_1, V_1, T)$ to the final state $(P_2, V_2, T)$ is equal to

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:

Work done by a system under isothermal change from a volume $V_1$ to $V_2$ for a gas which obeys Van der Waals' equation $(V - n\beta) \left( P + \frac{\alpha n^2}{V^2} \right) = nRT$.

Which of the accompanying $PV$ diagrams best represents an isothermal process?

$A$ sample of an ideal gas undergoes an isothermal expansion. If $dQ$,$dU$,and $dW$ represent the amount of heat supplied,the change in internal energy,and the work done respectively,then:

During an isothermal expansion of an ideal gas,