Which equation expresses the first law of thermodynamics for a closed system?

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

Answer: (C)

Energy conservation for a closed system means its internal energy changes only because energy is transferred as heat or as work. The sign convention used here treats heat added to the system as positive and work done by the system on its surroundings as positive. With that in mind, the internal energy rises when heat flows in, but drops when the system does work on its surroundings. Therefore the relationship is: ΔU = Q − W. This captures the idea that the energy gained from heat increases internal energy, while energy carried away by the system doing work reduces it. For example, if you add heat ten joules and the system does three joules of work, the internal energy increases by seven joules. If no heat is added but the system does work, ΔU becomes negative. The other forms either misplace the signs or mix up how heat and work contribute to internal energy.