The mathematical statement of the **first law of thermodynamics** is:
A$\Delta U = q - w$
B$\Delta U = q + w$
C$\Delta H = q_v$
D$\Delta G = \Delta H - T\Delta S$
Answer & 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.
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