State the first law of thermodynamics and its mathematical expression relating ΔU, q, and w.

• A. Energy is conserved; ΔU = q + w.
• B. Energy is created; ΔU = q - w.
• C. Energy is conserved; ΔU = q + w.
• D. Energy is destroyed; ΔU = w - q.

Answer: (C)

Energy cannot be created or destroyed; the change in a system’s internal energy comes from heat that flows into the system and from work done on the system. With the common chemistry sign convention, heat added to the system is positive and work done on the system is positive, so the first law is expressed as ΔU = q + w.

This means internal energy rises when you add heat or squeeze the system (do work on it), and it falls when the system does work on its surroundings (w becomes negative) or when heat leaves. For example, heating a gas at constant volume (no work) gives ΔU = q, since w = 0. If you compress the gas, w is positive and ΔU increases further; if the gas expands and does work on surroundings, w is negative, which can offset heat input.

The idea that energy is created or destroyed isn’t correct for this law. Some other sign conventions swap the sign of w, yielding ΔU = q − w, but in the common chemistry convention used here, the correct relation is ΔU = q + w.