It is required to raise the temperature of water of a swimming pool from `20^(@)C` to `25^(@)C` . The pool holds `10^(5) L` of water . How much energ in joules will be required ? Given that the specific heat of water is 4.184 `JK^(-1) g^(-1)`

Explanation

To solve the problem of how much energy is required to raise the temperature of the water in the swimming pool, we can use the formula:

\[ Q = mc\Delta T \]

where:
- \( Q \) = energy in joules
- \( m \) = mass of the water in grams
- \( c \) = specific heat capacity of water (4.184 J/K·g)
- \( \Delta T \) = change in temperature in Kelvin (or Celsius, since the size of the degree is the same)

### Step-by-Step Solution:

1. **Identify the parameters:**
- Initial temperature \( T_i = 20^\circ C \)
- Final temperature \( T_f = 25^\circ C \)
- Volume of water \( V = 10^5 \) L
- Specific heat capacity of water \( c = 4.184 \) J/K·g

2. **Calculate the change in temperature (\( \Delta T \)):**
\[ \Delta T = T_f - T_i = 25^\circ C - 20^\circ C = 5^\circ C \]

3. **Convert the volume of water to mass:**
- The density of water is approximately \( 1 \, \text{g/cm}^3 \) or \( 1000 \, \text{g/L} \).
- Therefore, the mass \( m \) can be calculated as:
\[ m = \text{density} \times \text{volume} = 1000 \, \text{g/L} \times 10^5 \, \text{L} = 10^8 \, \text{g} \]

4. **Substitute the values into the formula:**
\[ Q = mc\Delta T = (10^8 \, \text{g}) \times (4.184 \, \text{J/K·g}) \times (5 \, \text{K}) \]

5. **Calculate the energy required:**
\[ Q = 10^8 \times 4.184 \times 5 = 2.092 \times 10^9 \, \text{J} \]

### Final Answer:
The energy required to raise the temperature of the water from \( 20^\circ C \) to \( 25^\circ C \) is \( 2.092 \times 10^9 \) joules.