Find the heat required to convert 20 g of iceat `0^(@)C ` into water at the same temperature. ( Specific latent heat of fusion of ice `=80 cal//g ` )

Answer

To find the heat required to convert 20 g of ice at 0°C into water at the same temperature, we can use the formula for latent heat. The specific latent heat of fusion of ice is given as 80 cal/g.

### Step-by-Step Solution:

1. **Identify the mass of ice**:
- Given mass of ice = 20 g.

2. **Identify the specific latent heat of fusion**:
- Specific latent heat of fusion of ice = 80 cal/g.

3. **Use the formula for latent heat**:
- The formula to calculate the heat (Q) required for the phase change is:
\[ Q = m \times L_f \]
where:
- \( Q \) = heat required (in calories),
- \( m \) = mass of ice (in grams),
- \( L_f \) = specific latent heat of fusion (in cal/g).

4. **Substitute the values into the formula**:
- Here, \( m = 20 \, \text{g} \) and \( L_f = 80 \, \text{cal/g} \).
- Thus,
\[ Q = 20 \, \text{g} \times 80 \, \text{cal/g} \]

5. **Calculate the heat required**:
- Performing the multiplication:
\[ Q = 1600 \, \text{cal} \]

6. **Conclusion**:
- The heat required to convert 20 g of ice at 0°C into water at the same temperature is **1600 calories**.