A system releases 90 J of heat and has 30 J of work done by the surroundings. What is the change in internal energy?

Question

BlackTom AI · Accepted Answer

To tackle this problem, I’ll lay out the given quantities and apply the first law of thermodynamics, ΔU = q + w, with attention to sign conventions.
First, heat q is the energy transfer as heat into the system. Since the system releases heat, q = -90 J (negative means leaving the system).
Second, work w is the energy transfer as work done on the system. The statement says work is done by the surroundings, which means the system does not receive that work; rather, the surroundings do work on the system, so w = +30 J.
Now combine these to find the change in internal energy: ΔU = q + w = (-90 J) + (+30 J) = -60 J.
This means the system’s internal energy decreases by 60 J, and by conservation, the surroundings gain +60 J of energy.
Option-by-option check:
- Option 1: System: -30 J and Surrounding: +30 J. This would imply ΔU = -30 J, which mismatches the calculated -60 J, so it’s incorrect.
- Option 2: System: -120 J and Surrounding: +120 J. This suggests ΔU = -120 J, double the magnitude of the correct value, hence incorrect.
- Option 3: System: +60 J and Surrounding: -60 J. This would correspond to ΔU = +60 J, opposite in sign to the actual result, so it’s wrong.
- Option 4: System: -60 J and Surrounding: +60 J. This aligns with ΔU = -60 J for the system and +60 J for the surroundings, matching the energy bookkeeping correctly.
In summary, the correct energy accounting yields a −60 J change in the system’s internal energy and +60 J to the surroundings, which corresponds to option 4.

2254 CHEM 0101 SEC2010 HW 11

A system releases 90 J of heat and has 30 J of work done by the surroundings. What is the change in internal energy?

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