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* W* H\\\\V=10* 4* 3=120~m^3`

• mass of water :

ρ = 1000 kg/m³

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

• Heat required

c water = 4200 J/ kg ° C

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