Which expression represents the first law of thermodynamics for a system where W is work done by the system?

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

Answer: (D)

The change in a system’s internal energy comes from heat added minus the work the system does on its surroundings. Since W is defined as work done by the system, energy leaves as work, so you subtract W: ΔU = Q − W.

This means if you add heat but also let the system do work, the net change depends on the balance between Q and W. If Q equals W, ΔU is zero; if Q is greater, ΔU increases; if Q is smaller, ΔU decreases. The other expressions would reflect different sign conventions or ignore the work term, so they don’t match the stated convention.