The specific heat of a substance in the solid state is C1; its specific beat in the liquid state is C2 and its…

Analyze the question: A mass M of a substance changes from solid at temperature T to liquid at the same temperature T. The temperature does not change, so this is purely a change of state (melting).

Concept: When a substance changes state at constant temperature, the heat absorbed is latent heat, with no change in temperature. The heat needed is:

Q = mL

The specific heats C1 and C2 only matter when the temperature changes (Q = mcΔT). Here ΔT = 0, so those terms do not contribute.

Solution:

• Heating the solid: M × C1 × 0 = 0
• Melting at constant temperature: M × L
• Heating the liquid: M × C2 × 0 = 0

Total heat required: Q = ML

Checking the options:

• A and D involve T and C1/C2 in meaningless combinations, since no temperature change occurs.
• C (L) is the heat per unit mass, not for mass M.
• E includes temperature terms that don't apply.
• B (ML) matches our result.

Answer: B. ML

Tip: Always ask "does the temperature change?" If yes, use mcΔT. If it is a change of state at constant temperature, use mL. If both happen, add the two parts.