Does the internal energy of an ideal gas change in an isothermal process?

$A$ certain gas is isothermally compressed to $(1/3)^{rd}$ of its initial volume $(V_0 = 3 \ \text{L})$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \ \text{N/m}^2$, the magnitude of work done on the gas is . . . . . . $J$.

$A$ cylinder fitted with a piston contains $0.2 \, moles$ of air at a temperature of $27^{\circ}C$. The piston is pushed so slowly that the air within the cylinder remains in thermal equilibrium with the surroundings. Find the approximate work done by the system if the final volume is twice the initial volume (in $J$).

$Assertion :$ The isothermal curves intersect each other at a certain point.
$Reason :$ The isothermal change takes place slowly,so,the isothermal curves have very little slope.

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:

$A$ certain amount of heat supplied to an ideal gas under isothermal conditions will result in: