Because ΔU = 0 for both paths and ΔU = q + w, in each case q = −w. The
work of free expansion is zero (Section 2.3b), so in Path 1, w = 0 and therefore
q = 0 too. For Path 2, the work is given by eqn 2.10, so w=−nRT ln(Vf /Vi) and consequently
q = nRT ln(Vf /Vi).