2000 J of heat leaves the system and 2500 J of work is done on the system. What is the change in internal energy of the system (in Joule)?

Question

BlackTom AI · Accepted Answer

Using the first law of thermodynamics, ΔU = Q + W, where Q is heat added to the system and W is work done on the system.

1) Relevant knowledge points and concepts
- First law of thermodynamics: change in internal energy ΔU equals heat transferred into the system plus work done on the system.
- Sign convention: Q > 0 when heat enters the system, Q < 0 when heat leaves. W > 0 when work is done on the system (this convention makes ΔU = Q + W). An alternative common convention is ΔU = Q − W if W is taken as work done by the system; both give identical results if signs are applied consistently.

2) Step-by-step reasoning
- Heat leaves the system: Q = −2000 J (negative because energy leaves).
- Work of 2500 J is done on the system: W = +2500 J (positive because energy is added by work).
- Apply ΔU = Q + W.

3) Calculation (all intermediate steps)
ΔU = Q + W
ΔU = (−2000 J) + (+2500 J)
ΔU = −2000 J + 2500 J
ΔU = +500 J

4) Why the correct answer is correct
Because the system loses 2000 J of heat but gains 2500 J of mechanical energy from work, the net change in internal energy is the algebraic sum: a 2500 J gain minus a 2000 J loss = 500 J net gain. Positive ΔU means the internal energy increased.

5) Comment on possible alternative sign conventions / wrong interpretations
- If someone used ΔU = Q − W (with W interpreted as work done by the system), they must substitute W_by = −2500 J (since work is done on the system), giving ΔU = −2000 − (−2500) = +500 J. Any other numeric answer would result from inconsistent sign use.
- There are no multiple-choice options here, but common incorrect answers (e.g., −500 J or −4500 J) would come from reversing signs or adding magnitudes without sign attention.

6) Conclusion
The change in internal energy is +500 J, which matches the provided correct answer: 500 J.

2000 J of heat leaves the system and 2500 J of work is done on the system. What is the change in internal energy of the system (in Joule)?数值题

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