Question

If heat is supplied to an ideal gas in an isothermal process,
(a) the internal energy of the gas will increase
(b) the gas will do positive work
(c) the gas will do negative work
(d) the said process is not possible.

Answer 1

(b) the gas will do positive work

Internal energy of the gas, $U=\int C_{v}dT$
Here, Cv is the specific heat at constant volume and dT is the change in temperature.

If the process is isothermal, i.e. dT = 0, dU = 0.

Using the first law of thermodynamics, we get
$$\begin{gathered} \Delta Q=\Delta U+\Delta W \\ But\Delta U=0 \\ \Rightarrow \Delta Q=+\Delta W \end{gathered}$$

Here, $\Delta$W is the positive work done by the gas.