The quantity of heat required to convert 5kg of ice at its melting point to water without a change of temperature is

Answer Details

When a solid melts at its melting point, the heat supplied is used to break down the rigid arrangement of the particles rather than to raise the temperature, so a thermometer in the mixture stays at \(0\ ^\circ\text{C}\) throughout. Heat that produces a change of state at constant temperature is called latent heat, the word latent meaning hidden, because it produces no temperature reading.

The distinction the question turns on is between a total quantity and a per-kilogram quantity. The specific latent heat of fusion \(l\) is the heat needed to melt one kilogram of the solid at its melting point, with the unit \(\text{J kg}^{-1}\). The latent heat of fusion is the heat needed to melt the whole given mass, so

with the unit joule. Because the question fixes a definite mass of \(5\ \text{kg}\), the quantity described is the latent heat of fusion of that ice, not the specific latent heat. Naming it as the specific quantity would be wrong by a factor of \(5\).

The heat-capacity terms do not apply at all, because both describe heat that causes a temperature change: heat capacity is \(Q/\Delta\theta\) in \(\text{J K}^{-1}\) and specific heat capacity is \(Q/(m\Delta\theta)\) in \(\text{J kg}^{-1}\text{K}^{-1}\). Here the temperature does not change, so any formula containing \(\Delta\theta\) is ruled out immediately.

Carry two habits into the examination. First, the word specific always means per unit mass, so it can only be used when no particular mass is mentioned. Second, decide whether the heat causes a temperature change or a change of state: use \(Q = mc\Delta\theta\) for the first and \(Q = ml\) for the second.