Question

Three substances A, B and C of same mass are present at their respective melting points. On heating, if they melt completely in 5 minutes, 7 minutes and 3 minutes respectively, then which substance has the highest specific latent heat? (Assume heat is absorbed at the same rate)

• A. Substance A
• B. Substance B
• C. Substance C
• D. All the substances have same specific latent heat

Hint:

For a phase change at a constant rate of heating, the time taken is directly proportional to the specific latent heat of the substance.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify which substance has the highest specific latent heat of fusion, given that all substances have the same mass and are heated at the same rate, but take different times to melt completely.
Step 2: Key Formula or Approach:
The heat energy (\(Q\)) required to melt a substance at its melting point is given by the formula:
\[ Q = m \times L \] where \(m\) is the mass and \(L\) is the specific latent heat of fusion.
Also, if heat is supplied at a constant rate (\(P\)), then the heat absorbed in time (\(t\)) is:
\[ Q = P \times t \] Step 3: Detailed Explanation:
By equating the two expressions for heat (\(Q\)), we get:
\[ P \times t = m \times L \] The problem states that:
- The mass (\(m\)) is the same for all three substances.
- The rate of heat absorption (\(P\)) is the same for all three substances.
From the equation, we can write the specific latent heat (\(L\)) as:
\[ L = \frac{P \times t}{m} \] Since \(P\) and \(m\) are constants for this comparison, the specific latent heat (\(L\)) is directly proportional to the time (\(t\)) taken to melt.
\[ L \propto t \] This means the substance that takes the longest time to melt will have the highest specific latent heat.
The melting times are:
- Substance A: \(t_A = 5\) minutes
- Substance B: \(t_B = 7\) minutes
- Substance C: \(t_C = 3\) minutes
Since \(t_B>t_A>t_C\), it follows that \(L_B>L_A>L_C\).
Therefore, Substance B has the highest specific latent heat.
Step 4: Final Answer:
The substance that takes the longest time to melt (Substance B) has absorbed the most heat, and therefore has the highest specific latent heat.