63 kJ of heat was absorbed by a system, whilst also having 16 kJ of work done by it. 7 kJ of heat was then released by the system What is the change in the internal energy of this system after all these processes?

Question

BlackTom AI · Accepted Answer

The first law of thermodynamics, ΔU = Q − W, governs internal energy changes (ΔU) where Q is heat added to the system (positive when absorbed) and W is work done by the system (positive when the system does work on the surroundings).

Relevant quantities and sign conventions:
- Heat absorbed: Q1 = +63 kJ (adds energy).
- Work done by the system: W = +16 kJ (removes energy from the system).
- Heat released: Q2 = −7 kJ (removes energy).

Step-by-step reasoning and calculations:
1. Combine the two heat terms to get total heat transferred: Q_total = Q1 + Q2 = +63 kJ + (−7 kJ) = +56 kJ.
2. Apply the first law with W positive for work done by the system:
   ΔU = Q_total − W = 56 kJ − 16 kJ = 40 kJ.
3. Alternatively, proceed sequentially:
   - After absorbing 63 kJ and doing 16 kJ of work: ΔU1 = 63 − 16 = 47 kJ (net increase).
   - Then releasing 7 kJ of heat reduces internal energy: ΔU_total = 47 − 7 = 40 kJ.

Why the correct answer is correct:
- The system gains 63 kJ, loses 16 kJ as work, then loses another 7 kJ as heat, so the net gain is 63 − 16 − 7 = 40 kJ. This matches ΔU = Q − W with the proper sign convention.

Why the other options are incorrect:
- (a) An increase of 79 kJ: would correspond to adding 63 and 16 (63 + 16) incorrectly treating work done as added energy rather than subtracted.
- (b) A decrease of 47 kJ: wrong sign and magnitude; 47 kJ appears from 63 − 16 but that is an increase, not a decrease, and it ignores the −7 kJ step.
- (c) An increase of 47 kJ: equals the intermediate result after the first two processes but neglects the final 7 kJ heat release.

Conclusion: The net change in internal energy is an increase of 40 kJ, confirming answer d. An increase of 40 kJ.

63 kJ of heat was absorbed by a system, whilst also having 16 kJ of work done by it. 7 kJ of heat was then released by the system What is the change in the internal energy of this system after all these processes?单项选择题

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