Beregne tid

To solve this problem you need the density of water (using average value of ~1000 kg/m^3) and its heat capacity cP (using average value of ~4180 J/(kg*K)):

1) Get the volume (assuming the pool is completely filled) first and next the mass of water in the pool:

12 m * 6 m * 2 m = 141 m^3

141 m^3 * 1000 kg/m^3 = 144000 kg (mass of water in the pool)

3) The heat, Q, needed can be calculated from this equation:

Q = mass * cP* (T_final - T_initial)

Q = 144000 kg * 4180 J/(kg*K) * (25 deg C - 17 deg C) = 4.815*10^9 J (heat needed to raise the pool from 17 deg C to 25 deg C).

4) Get the time needed to heat the pool assuming not heat gets lost:

time = Q / P_input = 4.815*10^9 J / 5000 J/s = 9.63*10^5 s

That's about 11.15 days. Better get a stronger heater.

eller

Volume of pool = 12*6*2 = 144m³
Mass of water = 144,000kg
Specific heat of water = 4.186kJ/kg °C
Change in temperature = 8°C
Energy required = 144,000*4.186*8 = 4,822,272kJ

Power = energy/ time
Time = energy/ power
Time = 4,822,272kJ/5kW
Time = 964,454 seconds
Time = 964,454/3600 = 267.9 hours.
Time = 11.2 days