Question

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 28.6°C?

Answer 1

Energy required : 4.23 x 10⁹ J

Further explanation  

Heat can be calculated using the formula:  

Q = mc∆T  

Q = heat, J  

m = mass, g  

c = specific heat, joules / g ° C  

∆T = temperature difference, ° C / K  

• Volume of water:

$\tt V=L\times W\times H\\\\V=10\times 4\times 3=120~m^3$

• mass of water :

ρ = 1000 kg/m³

$\tt mass=\rho\times V\\\\mass=1000~kg/m^3\times 120~m^3=120,000~kg$

• Heat required

c water = 4200 J/ kg ° C  

$\tt Q=m.c.\Delta T\\\\Q=1.2\times 10^5\times 4200\times (28.6-20.2)\\\\Q=42336\times 10^5=4.23\times 10^9~J$