57 kJ of heat was absorbed by a system, whilst also having 24 kJ of work done on it. 7 kJ of heat was then released by the system What is the change in the internal energy of this system after these processes?

Question

BlackTom AI · Accepted Answer

First law of thermodynamics: ΔU equals the net heat transferred to the system plus the net work done on the system. Use the sign convention Q > 0 when heat is absorbed, and W_on > 0 when work is done on the system.

1) Relevant concepts
- Internal energy change ΔU is determined by energy entering or leaving the system as heat and work.
- Keep sign convention consistent: heat absorbed = positive Q, heat released = negative Q; work done on the system = positive W_on.

2) Step-by-step reasoning
- Heat absorbed initially: Q1 = +57 kJ (adds energy).
- Work done on system: W_on = +24 kJ (adds energy).
- Heat released later: Q2 = −7 kJ (removes energy).
- Total heat transferred Q_total = Q1 + Q2.

3) Calculations (all intermediate steps)
- Q_total = +57 kJ + (−7 kJ) = +50 kJ.
- ΔU = Q_total + W_on = 50 kJ + 24 kJ = 74 kJ.

4) Why this is correct
- Both the absorbed heat (+57 kJ) and the work done on the system (+24 kJ) increase internal energy, while the 7 kJ released reduces it. Summing these contributions gives the net increase of 74 kJ, which is exactly the internal energy change per the first law.

5) Why the other options are incorrect
- (a) A decrease of 33 kJ: incorrect sign and magnitude; it would correspond to subtracting work instead of adding and miscounting heat.
- (b) A decrease of 81 kJ: wrong sign and value; no combination of given numbers yields a net decrease of 81 kJ.
- (d) An increase of 81 kJ: corresponds to 57 + 24 but ignores the 7 kJ heat released, so it overestimates the increase by 7 kJ.

6) Conclusion
The net change in internal energy is an increase of 74 kJ, matching answer c. An increase of 74 kJ.

57 kJ of heat was absorbed by a system, whilst also having 24 kJ of work done on it. 7 kJ of heat was then released by the system What is the change in the internal energy of this system after these processes?单项选择题

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