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title: "A sample of mass \\(0.40 \\text{ kg}\\) of a pure solid at its melting point \\(273 \\text{ K}\\) is heated in an insulated container by a source that transfers energy to the sample at a constant rate \\(P\\). The graph shows the temperature \\(T\\) of the sample as a function of time \\(t\\). The specific heat capacity of the substance in its liquid phase is \\(2000 \\text{ J/(kg}\\cdot\\text{K)}\\). Based on the graph, what is the latent heat of fusion \\(L_f\\) of the substance?"
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url: "https://nerd-notes.com/ubq/117514/"
date_modified: "2026-08-04T06:52:31+00:00"
---

# A sample of mass \(0.40 \text{ kg}\) of a pure solid at its melting point \(273 \text{ K}\) is heated in an insulated container by a source that transfers energy to the sample at a constant rate \(P\). The graph shows the temperature \(T\) of the sample as a function of time \(t\). The specific heat capacity of the substance in its liquid phase is \(2000 \text{ J/(kg}\cdot\text{K)}\). Based on the graph, what is the latent heat of fusion \(L_f\) of the substance?

A sample of mass \(0.40 \text{ kg}\) of a pure solid at its melting point \(273 \text{ K}\) is heated in an insulated container by a source that transfers energy to the sample at a constant rate \(P\). The graph shows the temperature \(T\) of the sample as a function of time \(t\). The specific heat capacity of the substance in its liquid phase is \(2000 \text{ J/(kg}\cdot\text{K)}\). Based on the graph, what is the latent heat of fusion \(L_f\) of the substance?

![A Cartesian graph titled 'Temperature vs. Time' with the horizontal axis labeled 'Time t (s)' ranging from 0 to 200 with tick marks every 40 units (0, 40, 80, 120, 160, 200), and the vertical axis labeled 'Temperature T (K)' ranging from 270 to 320 with tick marks every 10 units (270, 280, 290, 300, 310, 320). A solid line starts at point (0, 273), remains horizontal along T = 273 K until t = 120 s, and then rises linearly from point (120, 273) to point (200, 313). Dashed grid lines extend from key points (120, 273) and (200, 313) to both axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826351-pJT0Za.jpg)

- **A.** \(4.8 \times 10^4 \text{ J/kg}\)
- **B.** \(8.0 \times 10^4 \text{ J/kg}\)
- **C.** \(9.6 \times 10^4 \text{ J/kg}\)
- **D.** \(1.2 \times 10^5 \text{ J/kg}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117514/*