If the latent heat of fusion of water is 350 kJ/kg, determine the quantity of latent heat given up by 15 kg of water at 0°C when it freezes into ice at 0°C.

Solution:

To determine the quantity of latent heat given up by 15 kg of water when it freezes into ice at 0°C, we can use the formula for latent heat of fusion:

${𝐿}_{𝑓}=\frac{𝑄}{𝑚}$

where:

• ${𝐿}_{𝑓}$ is the latent heat of fusion (given as 350 kJ/kg),
• $𝑄$ is the amount of heat energy absorbed or released during the phase change (which we need to find),
• $𝑚$ is the mass of the substance undergoing the phase change (given as 15 kg).

We can rearrange the formula to solve for $𝑄$:

$𝑄={𝐿}_{𝑓}\times 𝑚$

Substituting the given values, we get:

$𝑄=350\text{kJ/kg}\times 15\text{kg}$

$𝑄=5250\text{kJ}$

So, the quantity of latent heat given up by 15 kg of water when it freezes into ice at 0°C is 5250 kJ.