ΔH of reversible expansion of ideal gas

Question

Since its isothermal, $\delta U$ is zero. But enthalpy change $\delta H$ is $\delta U + \delta n(\text{gaseous})RT$ or $\delta H = \delta U + \delta (pV)$.

For reversible isothermal expansion of ideal gas, what is the $\delta H$, is it positive, negative or zero.

Ref: I've checked my study material and it says positive, which makes sense but my exam worksheets state it to be zero.

Answer 1

Recall that, for an ideal monatomic gas, $$U = \frac{3}{2}nRT.$$ (Diatomic and polyatomic gases have a larger coefficient.) For an isothermal expansion, reversible or otherwise, we therefore have $$\Delta H = \Delta(U+PV) = \Delta(U+nRT) = \frac{5}{2}nR\Delta T = 0,$$ since $\Delta T = 0$.