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.

In an isothermal process,the volume of an ideal gas is halved. One can say that:

If an ideal gas is compressed isothermally, which of the following statements is true?

The thermodynamic process,in which the internal energy of the system remains constant is ...........

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is ${m_A}$ and that in $B$ is ${m_B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then: