A system absorbs 30 J of heat and does 60 J of work; what is the change in internal energy ΔU?

• A. -60 J
• B. -30 J
• C. 0 J
• D. 60 J

Answer: (B)

Energy changes in a system come from heat added and work done by the system. The relation ΔU = Q − W uses Q as heat into the system and W as work done by the system. Here, heat absorbed is +30 J and the system does 60 J of work, so W = 60 J. Therefore ΔU = 30 − 60 = −30 J. The negative result means the internal energy decreases by 30 J, since more energy leaves as work than is gained as heat. (If one used a different sign convention for W, the formula would change, but with the standard ΔU = Q − W, this is the correct outcome.)