One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature,$27\,^{\circ}C$. The work done on the gas will be

For an isothermal expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to:

Can a system be heated and its temperature remain constant?

$Assertion :$ The isothermal curves intersect each other at a certain point.
$Reason :$ The isothermal changes take place rapidly,so the isothermal curves have very little slope.

$A$ 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?

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