What temperature change requires the same amount of heat as turning water into ice at its freezing point?

To determine the temperature change that requires the same amount of heat energy as turning water into ice at its freezing point, it is essential to consider the concept of heat transfer and phase changes. The heat required for phase changes, such as freezing, is quantified using the latent heat of fusion. For water, the latent heat of fusion is approximately 334 joules per gram. This means that to freeze 1 gram of water at 0ºC into ice at the same temperature, 334 joules of energy are removed.

The temperature change needed to match this heat removal can be calculated through the specific heat capacity of water, which is about 4.18 joules per gram per degree Celsius. To find the temperature change that corresponds to 334 joules, you can use the formula:

Heat (Q) = mass (m) × specific heat capacity (c) × temperature change (ΔT)

Rearranging the formula gives:

ΔT = Q / (m × c)

Assuming a mass of 1 gram for simplicity, the equation simplifies to:

ΔT = 334 joules / (1 gram × 4.18 joules/gram/ºC)

This results in:

ΔT = 79.94