The mathematical statement of the **first law of thermodynamics** is:
- $\Delta U = q - w$
- $\Delta U = q + w$
- $\Delta H = q_v$
- $\Delta G = \Delta H - T\Delta S$
Show answer and solution
Correct answer: B. $\Delta U = q + w$
The first law (with the IUPAC convention that w is work done **on** the system) reads $\Delta U = q + w$, expressing the conservation of energy for an isolated system.
$\Delta U = q - w$ uses the older convention where w is work done **by** the system.
$\Delta H = q_p$ (constant pressure, not $q_v$) and the Gibbs relation are different state equations.