LATENT HEAT OF FUSION PHYSICS
1. Mass of water=1.5 kg
T_c=30 celcius
Temperature of ice= 0 Celcius
Final temperature of water= 15 Celcius
Latent heat of fusion= 80 cal/g
L specific heat= 1 cal/g C
Mass of ice=?

To solve this problem, we need to balance the heat gained and lost in the system since heat will flow from the warmer water to the colder ice until thermal equilibrium is reached.

### Known Values
1. Mass of water, \( m_w = 1.5 \, \text{kg} = 1500 \, \text{g} \)
2. Initial temperature of water, \( T_{\text{water initial}} = 30^\circ \text{C} \)
3. Temperature of ice, \( T_{\text{ice}} = 0^\circ \text{C} \)
4. Final temperature of the system, \( T_{\text{final}} = 15^\circ \text{C} \)
5. Latent heat of fusion of ice, \( L_f = 80 \, \text{cal/g} \)
6. Specific heat of water, \( c = 1 \, \text{cal/g} \, ^\circ\text{C} \)

### Solution Strategy
1. **Calculate the heat lost by the water** cooling from its initial temperature to the final temperature.
2. **Calculate the heat gained by the ice** as it first melts, and then the resulting water warms up to the final temperature.
3. Set up an energy balance equation since heat lost by water will equal heat gained by the ice.

### Step 1: Heat Lost by Water (\( Q_{\text{water}} \))
Since water cools from \( 30^\circ \text{C} \) to \( 15^\circ \text{C} \):
\[
Q_{\text{water}} = m_w \cdot c \cdot (T_{\text{initial}} - T_{\text{final}})
\]
\[
Q_{\text{water}} = 1500 \, \text{g} \cdot 1 \, \text{cal/g}^\circ\text{C} \cdot (30^\circ \text{C} - 15^\circ \text{C})
\]
\[
Q_{\text{water}} = 1500 \cdot 15 = 22500 \, \text{cal}
\]

### Step 2: Heat Required to Melt Ice and Warm It to \( 15^\circ \text{C} \)
Let \( m_{\text{ice}} \) be the mass of ice in grams.

1. **Heat required to melt the ice at 0°C**:
   \[
   Q_{\text{melt}} = m_{\text{ice}} \cdot L_f
   \]
   \[
   Q_{\text{melt}} = m_{\text{ice}} \cdot 80 \, \text{cal/g}
   \]

2. **Heat required to warm the melted ice (now water) from \( 0^\circ \text{C} \) to \( 15^\circ \text{C} \)**:
   \[
   Q_{\text{warm}} = m_{\text{ice}} \cdot c \cdot (T_{\text{final}} - T_{\text{ice}})
   \]
   \[
   Q_{\text{warm}} = m_{\text{ice}} \cdot 1 \, \text{cal/g}^\circ\text{C} \cdot (15^\circ \text{C} - 0^\circ \text{C})
   \]
   \[
   Q_{\text{warm}} = m_{\text{ice}} \cdot 15
   \]

The total heat gained by the ice, \( Q_{\text{ice}} \), is:
\[
Q_{\text{ice}} = Q_{\text{melt}} + Q_{\text{warm}}
\]
\[
Q_{\text{ice}} = m_{\text{ice}} \cdot 80 + m_{\text{ice}} \cdot 15
\]
\[
Q_{\text{ice}} = m_{\text{ice}} \cdot (80 + 15) = m_{\text{ice}} \cdot 95
\]

### Step 3: Set Up the Energy Balance
Since \( Q_{\text{water}} = Q_{\text{ice}} \):
\[
22500 = m_{\text{ice}} \cdot 95
\]

Solving for \( m_{\text{ice}} \):
\[
m_{\text{ice}} = \frac{22500}{95}
\]
\[
m_{\text{ice}} \approx 236.84 \, \text{g}
\]

### Final Answer
The mass of the ice required is approximately **236.84 grams**.

Would you like further details or have questions on any part of this process?

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### Related Questions
1. How is latent heat different from specific heat?
2. What factors affect the amount of heat required to change the temperature of a substance?
3. How would the solution change if the initial temperature of the ice was below 0°C?
4. What is the significance of thermal equilibrium in heat transfer problems?
5. How does the specific heat of water compare to other common substances?

#### Tip
In heat transfer problems, carefully note the initial and final states of each substance. This helps set up an accurate energy balance.

LATENT HEAT OF FUSION PHYSICS 1. Mass of water=1.5 kg T_c=30 celcius Temperature of ice= 0 Celcius Final temperature of water= 15 Celcius Latent heat of fusion= 80 cal/g L specific heat= 1 cal/g C Mass of ice=?

This physics problem explores the calculation of the mass of ice that melts when placed in warm water. Given values include a water mass of 1.5 kg, an initial temperature of 30°C, and a final equilibrium temperature of 15°C. The latent heat of fusion is 80 cal/g, and the specific heat of water is 1 cal/g°C. Learn how to balance the energy equation and solve for the mass of the ice. Suitable for high school students (Grades 10-12).

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