Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by 1 Kelvin (or 1 degree Celsius). In this case, we are considering water in equilibrium with ice at constant pressure.

In equilibrium, the temperature remains constant, meaning that there is no change in the thermal energy of the system. Therefore, the molar heat capacity of water in equilibrium with ice is zero. This is because no heat is required to raise the temperature of the system since the temperature is constant.

However, it is important to note that the molar heat capacity of water in equilibrium with ice is not exactly zero. It is very close to zero but not exactly zero due to the small changes in temperature that may occur in the system.

The molar heat capacity of water in equilibrium with ice is approximately 40.45 J/K/mol. This value represents the heat capacity of water at very low temperatures, where the system is close to equilibrium.

The molar heat capacity of water at higher temperatures is different and is approximately 75.48 J/K/mol. This value represents the heat capacity of water when it is not in equilibrium with ice.

It is important to understand that the molar heat capacity of a substance can vary depending on the conditions under which it is measured. In this case, we are specifically considering water in equilibrium with ice at constant pressure.