If 15 kJ of heat is supplied to 25 kg of ice at 0°C, how many kilograms of ice will be melted into water?

Solution: To determine how many kilograms of ice will be melted into water when 15 kJ of heat is supplied to 25 kg of ice at 0°C, we can use the concept of latent heat of fusion.

Given:

• Latent heat of fusion of ice (${𝐿}_{𝑓}$) = 334 kJ/kg (at 0°C)
• Amount of heat supplied ($𝑄$) = 15 kJ
• Mass of ice ($𝑚$) = 25 kg

We can use the formula:

$𝑄={𝐿}_{𝑓}\times 𝑚$

to find the mass of ice melted (${𝑚}_{\text{melted}}$).

First, rearrange the formula to solve for ${𝑚}_{\text{melted}}$:

${𝑚}_{\text{melted}}=\frac{𝑄}{{𝐿}_{𝑓}}$

Now, plug in the given values:

${𝑚}_{\text{melted}}=\frac{15\text{kJ}}{334\text{kJ/kg}}\times 25\text{kg}$

${𝑚}_{\text{melted}}=\frac{15}{334}\times 25\text{kg}$

${𝑚}_{\text{melted}}\approx 1.41\text{kg}$

So, approximately 1.41 kilograms of ice will be melted into water when 15 kJ of heat is supplied to 25 kg of ice at 0°C.