Question

A substance of mass \( m \) requires a power input of \( P \) to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time \( t \). The latent heat of the substance is

• A. \( \frac{P t}{m} \)
• B. \( \frac{P m}{t} \)
• C. \( \frac{m}{P t} \)
• D. \( \frac{t}{P m} \)

Hint:

Latent heat is the energy required to change the state of a substance without changing its temperature.

Answer 1

The Correct Option is A

The latent heat \( L \) is the heat required to melt or solidify a substance. The amount of heat \( Q \) required is given by: \[ Q = m L \] This heat is supplied by the power \( P \) over a time \( t \), so: \[ Q = P t \] Equating both expressions: \[ m L = P t \] Solving for the latent heat \( L \): \[ L = \frac{P t}{m} \] Thus, the latent heat of the substance is \( \frac{P t}{m} \). 
Final Answer:  \( \frac{P t}{m} \).