If 1 kg of water ice and 1 kg of liquid water receive the same energy input, which will have a greater change in temperature?

The correct answer is that the liquid water will have a greater change in temperature when both receive the same energy input.

This can be understood through the concepts of specific heat capacity and phase change. Water in its liquid state has a specific heat capacity of approximately 4.18 J/g°C, meaning it requires a relatively large amount of energy to increase its temperature. In contrast, ice, while it also has a specific heat capacity, must first undergo a phase change if it is to be heated from ice to water. The energy input to ice at 0°C goes primarily into breaking the hydrogen bonds between water molecules rather than increasing the temperature, known as the heat of fusion.

Only after melting has occurred and we have transitioned from ice to liquid water can we then increase the temperature of the resulting water, which requires additional energy at the liquid phase. Therefore, the energy input goes primarily to changing the phase of the ice, and much less goes into raising its temperature while it is still ice. As a result, once both have been given the same amount of energy, the liquid water will demonstrate a greater change in temperature compared to the water ice.