When 10 g of coal is burnt, it raises the temperature of 2 litres of water from `20^(@)C` to `55^(@)C`. Calculate the heat of combustion of fuel.

Answer

To solve the problem of calculating the heat of combustion of coal based on the given data, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Given Data:**
- Mass of coal burnt, \( m_{\text{coal}} = 10 \, \text{g} \)
- Volume of water, \( V_{\text{water}} = 2 \, \text{litres} = 2000 \, \text{ml} \)
- Initial temperature of water, \( T_i = 20^\circ C \)
- Final temperature of water, \( T_f = 55^\circ C \)

2. **Calculate the Mass of Water:**
- Since the density of water is \( 1 \, \text{g/ml} \), the mass of water can be calculated as:
\[ m_{\text{water}} = V_{\text{water}} \times \text{density} = 2000 \, \text{ml} \times 1 \, \text{g/ml} = 2000 \, \text{g} \]

3. **Calculate the Change in Temperature:**
- The change in temperature \( \Delta T \) is given by:
\[ \Delta T = T_f - T_i = 55^\circ C - 20^\circ C = 35^\circ C \]

4. **Calculate the Heat Absorbed by Water:**
- The heat absorbed by the water can be calculated using the formula:
\[ Q = m_{\text{water}} \cdot c \cdot \Delta T \]
where \( c \) (specific heat of water) is \( 1 \, \text{cal/g}^\circ C \).
- Substituting the values:
\[ Q = 2000 \, \text{g} \cdot 1 \, \text{cal/g}^\circ C \cdot 35^\circ C = 2000 \cdot 35 = 70000 \, \text{cal} \]

5. **Calculate the Heat of Combustion per Gram of Coal:**
- The heat of combustion is defined as the amount of heat produced per gram of fuel. Since 10 g of coal produced 70000 cal:
\[ \text{Heat of combustion} = \frac{Q}{m_{\text{coal}}} = \frac{70000 \, \text{cal}}{10 \, \text{g}} = 7000 \, \text{cal/g} \]

### Final Answer:
The heat of combustion of the coal is \( 7000 \, \text{cal/g} \).