A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C. How much energy is required to raise the temperature of the water to 25.3°C?

Energy required to raise the temperature of water is 2.56x10⁹ J

Explanation:

We first need to find the volume of water in the pool.

10.0 m x 4.0 m x 3.0 m = 120 m³

Next, convert this to ml

120 m³ x 1x10⁶ = 120x10⁶ ml = 1.2x10⁸ ml

Now, if we assume that the density of the water is 1g/ml, we can estimate the mass of the water.

1.2x10⁸ ml x 1 g/ml = 1.2x10⁸ g

We can now use Q = mC∆T for find the energy needed to raise the temperature of this mass of water from 20.2ºC to 28.1ºC.

Q = heat = ?

m = mass = 1.2x10⁸ g

C = specific heat of water = 4.184 J/g/deg

∆T = change in temperature = 5.1ºC

Solving for Q: Q = (1.2x10⁸ g)(4.184 J/g/deg)(5.1 deg) = 2.56x10⁹ J  

Therefore, energy required to raise the temperature of water is 2.56x10⁹ J