---
title: "A \\(0.50\\text{ kg}\\) sample of a pure solid substance is heated at a constant rate in an insulated container. The graph shows the temperature \\(T\\) of the sample as a function of the total thermal energy \\(Q\\) added to it as it warms and undergoes a phase change to a liquid. What is the latent heat of fusion \\(L_f\\) of the substance, and how does the specific heat capacity of the solid phase \\(c_{\\text{solid}}\\) compare to that of the liquid phase \\(c_{\\text{liquid}}\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117454/"
date_modified: "2026-08-04T06:52:12+00:00"
---

# A \(0.50\text{ kg}\) sample of a pure solid substance is heated at a constant rate in an insulated container. The graph shows the temperature \(T\) of the sample as a function of the total thermal energy \(Q\) added to it as it warms and undergoes a phase change to a liquid. What is the latent heat of fusion \(L_f\) of the substance, and how does the specific heat capacity of the solid phase \(c_{\text{solid}}\) compare to that of the liquid phase \(c_{\text{liquid}}\)?

A \(0.50\text{ kg}\) sample of a pure solid substance is heated at a constant rate in an insulated container. The graph shows the temperature \(T\) of the sample as a function of the total thermal energy \(Q\) added to it as it warms and undergoes a phase change to a liquid. What is the latent heat of fusion \(L_f\) of the substance, and how does the specific heat capacity of the solid phase \(c_{\text{solid}}\) compare to that of the liquid phase \(c_{\text{liquid}}\)?

![A line graph showing Temperature T in degrees Celsius on the vertical axis versus Thermal Energy Added Q in kilojoules on the horizontal axis. The vertical axis ranges from 0 to 160 degrees Celsius with major grid lines and tick marks every 20 degrees Celsius. The horizontal axis ranges from 0 to 280 kilojoules with tick marks every 20 kilojoules. The graph consists of three connected straight line segments: the first segment goes from (0, 20) to (60, 80); the second segment is horizontal from (60, 80) to (140, 80); the third segment goes from (140, 80) to (260, 140). Grid lines clearly intersect at the four key data points (0, 20), (60, 80), (140, 80), and (260, 140). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826332-XP9dcK.jpg)

- **A.** \(L_f = 80\text{ kJ/kg}\); \(c_{\text{solid}} > c_{\text{liquid}}\)
- **B.** \(L_f = 280\text{ kJ/kg}\); \(c_{\text{solid}} < c_{\text{liquid}}\)
- **C.** \(L_f = 160\text{ kJ/kg}\); \(c_{\text{solid}} < c_{\text{liquid}}\)
- **D.** \(L_f = 160\text{ kJ/kg}\); \(c_{\text{solid}} > c_{\text{liquid}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117454/*