Q.In an adiabatic expansion of an ideal gas

Step 1. This question uses work $w$ in the sense of work done BY the expanding gas (the convention several other Indian textbooks and exam banks use, i.e. $\Delta U=q-w$), rather than this chapter's own IUPAC convention ($\Delta U=q+w$, $w$ = work done ON the system, Section 7.4.1).

Step 2. Under $\Delta U=q-w$ with $q=0$ (adiabatic): $\Delta U=-w \Rightarrow w=-\Delta U$ -- the gas does positive work on its surroundings exactly as its own internal energy falls. …

Recognise this question is phrased in the 'work done BY the system' sign convention, the …

• Trying to reconcile this with the chapter's own $\Delta U=q+w$ convention (Section 7.4.1, Case 3, which gives $\Delta U=w$) without noticing the sign of $w$ has flipped meaning between the tw …