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?

The work done to increase the volume of $2$ moles of an ideal gas from $V$ to $2V$ at a constant temperature $T$ is $W$. The work to be done to increase the volume of $2$ moles of the same gas from $2V$ to $4V$ at the same constant temperature $T$ is:

Obtain an expression for work done by an ideal gas in an isothermal expansion.

$A$ $500 \Omega$ 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 $\text{ cm/s}$)

$A$ 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.)