We have to determine whether the warming of ice from -10 °C to 0 °C results in more cooling or its melting at 0 °C.
The given values are:
Cs, ice = 2.09 J/g•°C
ΔHfusion = 6.02 kJ/mol
To solve this problem, we will calculate the energy that is required to warm 1 mol of ice from -10 °C to 0 °C and compare it with the heat of fusion of ice.
You just saw that the heat capacity of ice is Cs, ice = 2.09 J/g oC and that the heat of fusion of ice is 6.02 kJ/mol.
When a small ice cube at -10oC is put into a cup of water at room temperature, which of the following plays a greater role in cooling the liquid water: the warming of the ice from -10oC to 0oC , or the melting of the ice?