A swimming pool, \(10.0 \mathrm{~m}\) by \(4.0 \mathrm{~m}\), is filled with water to a depth of \(3.0 \mathrm{~m}\) at a temperature of \(20.2^{\circ} \mathrm{C}\). How much energy is required to raise the temperature of the water to \(24.6^{\circ} \mathrm{C} ?\)

= \(10.0\mathrm{~m} * 4.0\mathrm{~m} * 3.0\mathrm{~m} = 120\mathrm{~m^3}\) #tag_title# Step 2: Calculate the mass of the water #tag_content# To calculate the mass of the water, we need to know the volume (V) and the density (\(\rho\)) of the water. The density of water is approximately \(1000\mathrm{~kg/m^3}\). The mass (m) of the water can be calculated as: m = V * \(\rho\) = \(120\mathrm{~m^3} * 1000\mathrm{~kg/m^3} = 120,000\mathrm{~kg}\) #tag_title# Step 3: Apply the formula for calculating the energy required to heat the water #tag_content# To calculate the energy (Q) required to raise the temperature of the water, we need to know the mass (m) of the water, the specific heat capacity (c) of the water, and the temperature change (\(\Delta T\)). The specific heat capacity of water is approximately \(4.18\mathrm{~kJ/kg\cdot K}\). The temperature change can be calculated as the final temperature minus the initial temperature: \(\Delta T = 24.6^{\circ}\mathrm{C} -20.2^{\circ}\mathrm{C}= 4.4\mathrm{^{\circ}C}\). The energy required (Q) can be calculated as: Q = m * c * \(\Delta T\) = \(120,000\mathrm{~kg} * 4.18\mathrm{~kJ/kg\cdot K} * 4.4\mathrm{~K} = 2,203,776\mathrm{~kJ}\) Thus, the energy required to raise the temperature of the water to \(24.6^{\circ}\mathrm{C}\) is \(2,203,776\mathrm{~kJ}\).