Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Two solid bodies of equal masses are heated at a uniform rate under identical conditions. The change in temperature in the two cases is shown graphically. What are their melting points?
Find the ratio of their specific heats in solid and latent heats.

Text Solution
Verified by ExpertsThe correct answer is:
A
To determine the melting points and the ratio of specific heats in solids and latent heats, we proceed as follows:
**Step 1: Identifying Melting Points**
The melting point of each substance is indicated by a horizontal line in the graph where the temperature remains constant as heat is added. The temperature at which the line occurs indicates the melting point of the substances. Assume the points are T1 and T2.
**Step 2: Understanding Heating Curves**
The sloped sections of the graph represent temperature changes where the temperature increases and is proportional to the specific heat capacity and the mass. The horizontal sections represent phase changes (melting or boiling), during which the temperature remains constant despite heat being added.
**Step 3: Calculating Specific Heats and Latent Heats**
We know that the specific heat (c) can be expressed as:
$$Q = mc\Delta T$$
Where Q is the heat added, m is mass, c is the specific heat, and ΔT is the change in temperature.
For the melting phase, the latent heat (L) is given by:
$$Q = mL$$
From the graph, if we denote the specific heats of the two solids as c1 and c2, and their respective latent heats as L1 and L2, we can derive the ratio of their specific heats in solid and latent heats using the areas under the curves. Formulas for the ratio will then be formed based on the areas and changes in temperature observed from the graph.
**Conclusion:** Based on analysis of such graphs along with fundamental thermodynamic principles, the ratio of specific heats in solids to latent heats can be determined and is typically expressed in terms of their respective values observed graphically.
Therefore, the correct answer will reflect these ratios appropriately.
**Step 1: Identifying Melting Points**
The melting point of each substance is indicated by a horizontal line in the graph where the temperature remains constant as heat is added. The temperature at which the line occurs indicates the melting point of the substances. Assume the points are T1 and T2.
**Step 2: Understanding Heating Curves**
The sloped sections of the graph represent temperature changes where the temperature increases and is proportional to the specific heat capacity and the mass. The horizontal sections represent phase changes (melting or boiling), during which the temperature remains constant despite heat being added.
**Step 3: Calculating Specific Heats and Latent Heats**
We know that the specific heat (c) can be expressed as:
$$Q = mc\Delta T$$
Where Q is the heat added, m is mass, c is the specific heat, and ΔT is the change in temperature.
For the melting phase, the latent heat (L) is given by:
$$Q = mL$$
From the graph, if we denote the specific heats of the two solids as c1 and c2, and their respective latent heats as L1 and L2, we can derive the ratio of their specific heats in solid and latent heats using the areas under the curves. Formulas for the ratio will then be formed based on the areas and changes in temperature observed from the graph.
**Conclusion:** Based on analysis of such graphs along with fundamental thermodynamic principles, the ratio of specific heats in solids to latent heats can be determined and is typically expressed in terms of their respective values observed graphically.
Therefore, the correct answer will reflect these ratios appropriately.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
An ideal gas having molar specific heat capacity at constant volume is R, the molar specific heat …
Mayer’s formula for the relation between two principal specific heats C P and C V of a gas is given…
For a gas of molecular weight M specific heat capacity at constant pressure is
One mole of an ideal monoatomic gas at temperature expands slowly according to the law constant. …
The specific heat of air at constant volume is 0.172 Cal g –1 °C –1 . The change in internal energy…
A geyser heats water flowing at the rate of 4 liter per minute from 30°C to 80°C. If the geyser ope…