Question

Molar heat capacity of water in equilibrium with ice at constant pressure is:
A. Zero.
B. \[\infty \]
C. \[40.45\;{\rm{KJ}}\;{{\rm{K}}^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}\]
D. \[75.48\;{\rm{J}}\;{{\rm{K}}^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}\]

Answer 1

Hint: Molar heat capacity is usually given in \[{\rm{J/mol}} \cdot {\rm{K}}\]. This basically means how much energy you need to raise the temperature of 1 mole of substance by 1K. If we increase or decrease the amount of water then heat requirements may also increase or decrease respectively.

Complete step by step answer
Heat capacity is the amount of heat added to a substance to raise its temperature by one Kelvin, we can say that heat capacity is nothing but the amount of heat which is to supplied to increase the temperature of \[{\rm{1}}\;{\rm{kg}}\] of a substance by one Kelvin. It has unit \[{\rm{J/mol}} \cdot {\rm{K}}\].
The question says molar heat capacity of water in equilibrium with ice at constant pressure is,
Heat capacity at constant pressure = \[{\left( {\dfrac{{\partial H}}{{\partial T}}} \right)_P}\]
We know that at constant pressure, water is in equilibrium with ice, \[\partial H\] is supplied to the system, when the temperature changes to \[\partial T\] is zero. Then the heat supplied is utilized for the phase transition. At a constant pressure, when \[\partial H\] is provided to the system, water is in equilibrium. When temperature changes to \[\partial T\] is zero, then the heat supplied for the utilization of the phase transition. Therefore, molar heat capacity of water in equilibrium with ice at constant pressure is infinite.

Therefore, the correct answer is B.

Note :
Water has a high specific heat capacity, with a bent structure. It is rotationally asymmetric, so it can hold more energy than other symmetry molecules in the rotational degree of freedom. And the more important reason is the hydrogen bond, when hydrogen atoms bind with a more electronegative atom. Its electron contains high probability to be found in the vicinity of the oxygen atom.