State the first law of thermodynamics for a closed system.

• A. ΔU = Q − W
• B. ΔU = W − Q
• C. Q = ΔU − W
• D. ΔU = Q + W

Answer: (A)

The first law for a closed system is an energy balance: the change in the system’s internal energy equals the heat added to the system minus the work the system does on its surroundings. With the common convention that heat added is positive and work done by the system is positive, this becomes ΔU = Q − W.

This makes intuitive sense: supplying heat increases the internal energy, while the system doing work (like expanding a piston) uses up some of that energy, reducing ΔU by the amount of work W. For example, if you add 100 J of heat and the system does 30 J of work, the internal energy rises by 70 J.

The other expressions correspond to different sign conventions. ΔU = W − Q would flip the effect of heat input on ΔU, and Q = ΔU − W rearranges to ΔU = Q + W, which aligns with a convention where W is defined as work done on the system. The form ΔU = Q − W is the standard form used here.