During which thermodynamic process does $T$ remain constant, while the other two variables $P$ and $V$ change?

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

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

In an isothermal change, an ideal gas obeys:

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

$Assertion :$ 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.