Suppose Q and W denote the amount of heat supplied to an ideal gas...

According to the first law of thermodynamics, $Q = \Delta U + W$.

For an ideal gas, the internal energy depends only on its absolute temperature.

In an isothermal process, the temperature of the gas remains constant, which implies $\Delta T = 0$.

Consequently, the change in internal energy $\Delta U = 0$.

Substituting this into the first law equation yields $Q = W$.

Thus, the heat supplied to the ideal gas is equal to the work performed by it.