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

$A$ $500 \Omega$ resistor connected to an external battery is placed inside a thermally insulated cylinder fitted with a frictionless piston. The cylinder contains an ideal gas. $A$ current $i$ of $200 \text{ mA}$ flows through the resistor as shown in the figure. The mass of the piston is $10 \text{ kg}$. Assuming $g = 10 \text{ m/s}^2$, the speed at which the piston will move upward, due to heat dissipated by the resistor, so that the temperature of the gas remains unchanged is (in $\text{ cm/s}$)

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

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:

In an isothermal process,which statement is wrong?

An isothermal process has a non-linear graph between: