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The problem you've uploaded is a thermodynamics question involving the heat exchange between melting ice and water. Here's the setup:

### Given Data:
- Mass of ice block = \( 0.05 \, \text{kg} \)
- Mass of water = \( x \, \text{kg} \)
- Initial temperature of both ice and water = \( 0^\circ \text{C} \)
- Final temperature of the mixture = \( 4^\circ \text{C} \)
- Energy supplied to the mixture = \( 25,000 \, \text{J} \)

### Assumptions and Constants:
1. **Latent heat of fusion of ice** \( L_f = 334,000 \, \text{J/kg} \) (energy required to convert 1 kg of ice at \( 0^\circ \text{C} \) into water without temperature change).
2. **Specific heat capacity of water** \( c_w = 4,200 \, \text{J/kg}^\circ \text{C} \) (energy required to raise the temperature of 1 kg of water by \( 1^\circ \text{C} \)).

### Heat Calculations:

1. **Heat required to melt the ice**:
   \[
   Q_1 = m_{\text{ice}} \times L_f = 0.05 \times 334,000 = 16,700 \, \text{J}
   \]
   This is the energy needed to melt the ice.

2. **Heat required to raise the temperature of the melted ice from \( 0^\circ \text{C} \) to \( 4^\circ \text{C} \)**:
   \[
   Q_2 = m_{\text{ice}} \times c_w \times \Delta T = 0.05 \times 4,200 \times 4 = 840 \, \text{J}
   \]
   This is the energy needed to raise the temperature of the melted ice (now water) to \( 4^\circ \text{C} \).

3. **Heat required to raise the temperature of the water from \( 0^\circ \text{C} \) to \( 4^\circ \text{C} \)**:
   \[
   Q_3 = m_{\text{water}} \times c_w \times \Delta T = x \times 4,200 \times 4 = 16,800x \, \text{J}
   \]
   This is the energy needed to raise the temperature of the water to \( 4^\circ \text{C} \).

### Total Energy Supplied:
\[
Q_{\text{total}} = Q_1 + Q_2 + Q_3
\]
Given that \( Q_{\text{total}} = 25,000 \, \text{J} \), we have:
\[
25,000 = 16,700 + 840 + 16,800x
\]
Simplifying:
\[
25,000 = 17,540 + 16,800x
\]
\[
25,000 - 17,540 = 16,800x
\]
\[
7,460 = 16,800x
\]
\[
x = \frac{7,460}{16,800} \approx 0.444 \, \text{kg}
\]

### Final Answer:
The mass of the water is approximately \( 0.444 \, \text{kg} \).

Let me know if you'd like more details or have any questions. Here are some related questions for further understanding:

1. How is the specific heat capacity of water crucial in this problem?
2. What is the latent heat of fusion, and how is it different from specific heat?
3. Why doesn't the ice raise in temperature until it is fully melted?
4. How would the result change if the final temperature were \( 10^\circ \text{C} \) instead of \( 4^\circ \text{C} \)?
5. Could this process occur without the addition of external energy? Why or why not?

**Tip:** Always ensure that units are consistent when calculating energy, mass, or temperature changes to avoid mistakes in thermodynamic problems.

A melting ice block of mass 0.05 kg is mixed with x kg of water at 0°C in a well-insulated container. If 25,000 J of energy is supplied to the mixture, the mixture changes to water at 4°C. Find the value of x.

Solve a thermodynamics problem involving the heat exchange between a melting ice block and water. Learn how to calculate the mass of water when 25,000 J of energy is supplied. This solution covers key concepts such as heat transfer equations and latent heat, suitable for high school students (Grades 9-12).

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