One kg of ice at `0^(@)C` is mixed with 1 kg of water at `10^(@)C`. The resulting temperature will be

Options

A. between `0^(@)C` and `10^(@)C`
B. `0^(@)C`
C. less than `0^(@)C`
D. greater than `0^(@)C`

Explanation

To solve the problem of mixing 1 kg of ice at 0°C with 1 kg of water at 10°C, we need to analyze the heat transfer between the two substances. Here's the step-by-step solution:

### Step 1: Identify the heat required to melt the ice
The latent heat of fusion for ice is approximately 80 kcal/kg. Since we have 1 kg of ice, the total heat required to melt the ice completely is:
\[ Q_{\text{ice}} = m \cdot L = 1 \, \text{kg} \cdot 80 \, \text{kcal/kg} = 80 \, \text{kcal} \]

### Step 2: Identify the heat released by the water
The specific heat of water is approximately 1 kcal/kg°C. The water is initially at 10°C, and it can cool down to 0°C. The heat released by the water as it cools from 10°C to 0°C is given by:
\[ Q_{\text{water}} = m \cdot c \cdot \Delta T = 1 \, \text{kg} \cdot 1 \, \text{kcal/kg°C} \cdot (10 - 0) \, \text{°C} = 10 \, \text{kcal} \]

### Step 3: Compare the heat required and the heat available
Now we compare the heat required to melt the ice (80 kcal) with the heat available from the water (10 kcal):
- Heat required to melt ice: 80 kcal
- Heat released by water: 10 kcal

Since the heat released by the water (10 kcal) is less than the heat required to melt the ice (80 kcal), not all the ice will melt.

### Step 4: Determine the final temperature
Because the heat released by the water is insufficient to melt all the ice, the final temperature of the mixture will remain at 0°C. The water will cool down to 0°C, and the ice will absorb the heat until it partially melts, but the temperature of the system will not rise above 0°C.

### Final Answer:
The resulting temperature of the mixture is **0°C**.

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