A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change in internal energy is ____________ J. (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Give each energy flow its sign first: heat coming in is plus, work done by the system is minus.

1. Sign convention. In chemistry the first law is written Δ U = q + w, where w is work done on the system. Heat absorbed by the system is positive, and work done by the system is negative.
2. Assign the signs. The system absorbs heat, so q = +150 J. The system does work, so w = -200 J.

   Δ U = q + w = 150 + (-200) = -50 J

3. So. The internal energy falls by 50 J, because the system gave out more energy as work than it took in as heat. The magnitude is 50.

The common slip: 350. Treating the work done by the system as positive gives 150 + 200 = 350 J, not 50.

The idea to keep. Before you add anything in the first law, mark each term: heat in is positive, work done by the system is negative. The minus sign on Δ U just tells you the energy went down.

Answer from the NTA final answer key. Solution by PrepWiser.