The condition $dQ = dW$ holds good in which of the following?

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

Two ideal gases $A$ and $B$ of the same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such that the pressure of gas $A$ decreases by $50 \%$ and the pressure of gas $B$ decreases by $75 \%$. If the work done by both the gases is same, then $T_1: T_2$ is:

$A$ perfect gas of volume $5 \ L$ is compressed isothermally to a volume of $1 \ L$. The $r.m.s.$ speed of the molecules will

Can the change in internal energy of an ideal gas be non-zero during an isothermal process?

$A$ vertical cylinder with heat-conducting walls is closed at the bottom and is fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature,$T_0$. The piston is moved up slowly to increase the volume of the gas to $\eta$ times. Which of the following is incorrect?