Question

Two substances A and B of the same mass are heated at a constant rate. The variation of temperature θ of the substances with time t is shown in the figure. Choose the correct statement

• A. Specify heat of A is greater than that of B
• B. Specify heat of B is greater than that of A
• C. Both have some specific heat
• D. None of the above is true

Answer 1

The Correct Option is A

We are given: 

• Melting point of Substance A = 60°C
• Melting point of Substance B = 20°C
• Time taken to melt:
  • Substance A: 4 minutes
  • Substance B: 2.5 minutes

During melting (fusion), the temperature of a substance remains constant, and the heat supplied is used entirely to overcome the intermolecular forces. This energy is measured by the latent heat of fusion.

Now, since both substances are subjected to the same heat source (assumption), and substance A takes more time to melt than substance B, it implies that more heat is required to melt A completely than B.

Heat required for melting is given by:

Q = mL

Where:

• m is mass (assumed equal)
• L is latent heat of fusion

So, longer time to melt → higher heat requirement → greater latent heat of fusion. And since specific latent heat (heat per unit mass) is higher, it follows that:

Specific heat of A is greater than that of B

The correct option is (A): Specific heat of A is greater than that of B

Answer 2

Given:

• Substance A: Melting point = 60°C, Time to melt = 4 minutes 
• Substance B: Melting point = 20°C, Time to melt = 2.5 minutes

During fusion (melting), a substance absorbs heat to change its state from solid to liquid without a change in temperature. The amount of heat absorbed depends on:

• The specific latent heat of fusion (energy required per unit mass to melt)
• The duration of heating, assuming constant heat supply

Since substance A takes more time (4 min) to melt compared to substance B (2.5 min), under the assumption of same heat input rate, substance A absorbs more heat.

This indicates that substance A has a higher specific latent heat than substance B. A greater specific latent heat suggests that substance A requires more energy to melt a unit mass, hence a greater specific heat.

Therefore, the correct conclusion is:

Option (A): Specific heat of A is greater than that of B