2.1 kJ of heat was absorbed by a system, whilst also having 9.2 kJ of work done by it. What is the change in the internal energy of this system after these processes?

Question

BlackTom AI · Accepted Answer

First law of thermodynamics: ΔU = Q − W, where Q is heat added to the system and W is work done by the system. This equation gives the change in internal energy (ΔU).

Relevant points:
- Heat absorbed by the system is positive: Q = +2.1 kJ.
- Work done by the system is positive in the Q − W convention: W = +9.2 kJ.
- A negative ΔU means the system’s internal energy decreases.

Step-by-step reasoning and arithmetic:
1. Start with the formula: ΔU = Q − W.
2. Substitute the given values: ΔU = (+2.1 kJ) − (+9.2 kJ).
3. Compute the difference: 2.1 − 9.2 = −7.1.
4. So ΔU = −7.1 kJ.

Intermediate steps shown:
- Q = +2.1 kJ
- W = +9.2 kJ
- ΔU = 2.1 kJ − 9.2 kJ = −7.1 kJ

Why this is correct:
Because the system does more work (9.2 kJ) than the heat it absorbs (2.1 kJ), the excess energy leaving as work reduces the internal energy, giving a negative change. Using the alternative sign convention ΔU = Q + W' where W' is work done on the system, W' = −9.2 kJ, so ΔU = 2.1 + (−9.2) = −7.1 kJ — the same numerical result, confirming consistency.

Other possible misunderstandings:
- If someone mistakenly treated work done by the system as negative while still using ΔU = Q − W, they would get the wrong sign. Correct use of sign convention as shown yields −7.1 kJ.

Conclusion:
The change in internal energy is −7.1 kJ, which matches the provided answer: -7.1 kJ.

2.1 kJ of heat was absorbed by a system, whilst also having 9.2 kJ of work done by it. What is the change in the internal energy of this system after these processes?数值题

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