Question

Molar heat capacity of water in equilibrium with ice at constant pressure is
(A) Zero
(B) Infinity
(C) $40.45{k^{ - 1}}mo{l^{ - 1}}$
(D) None

Answer 1

The heat capacity of a body can be taken as the amount of heat required to raise the temperature of the body through$1K$. The amount of heat required to increase the temperature of one mole of the substance through $1K$ is called the molar heat capacity of that substance. It can be taken as the product of the mass of the substance and specific heat capacity of the substance.

Complete step by step solution:
The temperature at which, both liquids and solids coexist in thermal equilibrium is called the melting point.
Therefore, we can say that the point where water and ice coexist is the melting point.
The temperature can be taken as the melting point temperature of water at that pressure.
The heat capacity can be written as,
$S = \dfrac{{\Delta Q}}{{\Delta T}}$
Where $S$stands for the heat capacity of the substance, $\Delta Q$is the amount of heat absorbed or rejected by the substance, and $\Delta T$stands for the change in temperature.
Since the ice and water are in equilibrium,
$\Delta T = 0$
But the heat exchange $\Delta Q \ne 0$
Therefore, the heat capacity will be, $\dfrac{{\Delta Q}}{{\Delta T}} = \dfrac{{\Delta Q}}{0} = \infty$
The molar heat capacity will be infinity at the melting point of water.

The answer is Option (B): Infinity

Note:
The melting point of a substance at standard atmospheric pressure is called the normal melting point. The melting point of a body will depend on the pressure. If we heat a liquid its temperature will rise. At a particular temperature the liquid changes to a gaseous state. This temperature is called the boiling point. The temperature remains steady until the whole liquid Is changed into a vapor state.