To solve the problem of mixing 100g of ice at 0°C with 100g of water at 100°C, we need to follow these steps:
### Step 1: Calculate the heat required to melt the ice.
The heat required to melt the ice (Q1) can be calculated using the formula:
\[ Q_1 = m \cdot L_f \]
where:
- \( m \) = mass of ice = 100g
- \( L_f \) = latent heat of fusion of ice = 80 cal/g
Substituting the values:
\[ Q_1 = 100 \, \text{g} \times 80 \, \text{cal/g} = 8000 \, \text{cal} \]
### Step 2: Calculate the heat released by the water as it cools down.
The heat released by the water (Q2) when it cools from 100°C to 0°C can be calculated using the formula:
\[ Q_2 = m \cdot S \cdot \Delta T \]
where:
- \( m \) = mass of water = 100g
- \( S \) = specific heat of water = 1 cal/g°C
- \( \Delta T \) = change in temperature = 100°C - 0°C = 100°C
Substituting the values:
\[ Q_2 = 100 \, \text{g} \times 1 \, \text{cal/g°C} \times 100 \, \text{°C} = 10000 \, \text{cal} \]
### Step 3: Determine the excess heat available after melting the ice.
Now we find the excess heat available after the ice has melted:
\[ \text{Excess Heat} = Q_2 - Q_1 = 10000 \, \text{cal} - 8000 \, \text{cal} = 2000 \, \text{cal} \]
### Step 4: Calculate the final temperature of the mixture.
After the ice has melted into water at 0°C, we have a total of 200g of water (100g from melted ice and 100g from the original water). The excess heat will now be used to raise the temperature of this 200g of water.
Using the formula:
\[ Q_3 = m \cdot S \cdot \Delta T \]
where:
- \( Q_3 = 2000 \, \text{cal} \)
- \( m = 200 \, \text{g} \)
- \( S = 1 \, \text{cal/g°C} \)
We need to find \( \Delta T \):
\[ 2000 \, \text{cal} = 200 \, \text{g} \times 1 \, \text{cal/g°C} \times \Delta T \]
\[ \Delta T = \frac{2000 \, \text{cal}}{200 \, \text{g}} = 10 \, \text{°C} \]
### Step 5: Calculate the final temperature.
Since the initial temperature of the mixture (after melting the ice) is 0°C, the final temperature (Tf) will be:
\[ T_f = T_i + \Delta T = 0 \, \text{°C} + 10 \, \text{°C} = 10 \, \text{°C} \]
### Final Result:
The resultant temperature of the mixture is **10°C**.
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