The graph below shows the variation in temperature for 0.6 kg of a solid substance transitioning to a gas as energy is added to it. Of all the energy added, 1kJ was lost to the surroundings. What is the latent heat of fusion for this substance in [math: kJ/kg] ?

Question

BlackTom AI · Accepted Answer

The plateau corresponding to melting (latent heat of fusion) is the flat section where temperature stays constant while energy is added. On the graph this flat section runs from energy added = 4.0 × 10^3 J to 7.0 × 10^3 J, so the energy absorbed during fusion is the difference 7.0 − 4.0 = 3.0 × 10^3 J (3.0 kJ).

1) Relevant concepts
- Latent heat of fusion Lf is the energy required to change 1 kg of a substance from solid to liquid at its melting temperature: Q = m Lf.
- On a temperature vs energy graph, a horizontal (constant T) segment indicates a phase change; the horizontal length (difference in energy) is the energy used for that phase change.
- The problem states 1 kJ of the energy supplied was lost to the surroundings; this loss is given as part of the total energy bookkeeping but does not change the energy represented by the plateau segment (the plotted energy differences show the energy actually used by the sample during each process).

2) Step-by-step reasoning and calculation
- Read off energy used during the melting plateau: Q_fusion = (7.0 − 4.0) × 10^3 J = 3.0 × 10^3 J.
- Mass m = 0.6 kg.
- Use Q = m Lf → Lf = Q / m = (3.0 × 10^3 J) / (0.6 kg).

3) Intermediate arithmetic
- 3.0 × 10^3 J ÷ 0.6 kg = 5.0 × 10^3 J/kg = 5.0 kJ/kg.

4) Why this is correct
- The horizontal segment from 4.0 to 7.0 × 10^3 J is the melting interval, so the 3.0 kJ shown is the energy absorbed to melt 0.6 kg. Dividing absorbed energy by mass gives the latent heat of fusion. The stated 1 kJ loss refers to energy not delivered to the system overall, but the graph’s plateau energy difference already represents the energy going into the phase change, yielding 3.0 kJ for the fusion step.

5) Why the other options are incorrect
- b (1.7 kJ/kg): would correspond to only 1.0 kJ used for fusion (1.0/0.6 ≈1.67 kJ/kg), inconsistent with the plateau length.
- c (6.7 kJ/kg): would correspond to ≈4.0 kJ used for fusion, but the graph shows 3.0 kJ.
- d (3.3 kJ/kg): corresponds to 2.0 kJ used for fusion (2.0/0.6 ≈3.33 kJ/kg), which is the length of a different plateau; it does not match the melting plateau used here.

6) Conclusion
The latent heat of fusion is 5.0 kJ/kg, matching answer (a).

The graph below shows the variation in temperature for 0.6 kg of a solid substance transitioning to a gas as energy is added to it. Of all the energy added, 1kJ was lost to the surroundings. What is the latent heat of fusion for this substance in [math: kJ/kg] ?单项选择题

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