Question

5,000 Joules of heat is added to ice at 273 K. All the heat goes into changing solid ice into liquid water. How much ice is melted? The heat of fusion of water is 3.34×105 J/kg.

Answer 1

To calculate how much ice is melted when 5,000 Joules of heat is added, we can use the formula for heat transfer during phase change:

\[
Q = m \cdot L_f
\]

Where:
- \(Q\) is the heat added (in Joules),
- \(m\) is the mass of the ice melted (in kg),
- \(L_f\) is the heat of fusion of water (in J/kg).

Given:
- \(Q = 5000 \, \text{J}\)
- \(L_f = 3.34 \times 10^5 \, \text{J/kg}\)

We can rearrange the formula to solve for \(m\):

\[
m = \frac{Q}{L_f}
\]

Substituting in the values:

\[
m = \frac{5000 \, \text{J}}{3.34 \times 10^5 \, \text{J/kg}}
\]

Calculating \(m\):

\[
m = \frac{5000}{334000} \approx 0.01497 \, \text{kg}
\]

Thus, the mass of ice melted is approximately \(0.01497 \, \text{kg}\) or \(14.97 \, \text{grams}\).