Applying Q = m x c x change in T to find the energy and time to heat stored water.
The calculation that underpins sizing
The energy needed to raise the temperature of stored water comes from Q = m x c x change in T, where m is the mass in kilograms, c is the specific heat capacity and change in T is the temperature rise. For water, one litre is about one kilogram and c is about 4.186 kJ per kilogram per °C. The figures below are chosen to show the method.
The situation. A 150 litre cylinder (about 150 kg of water) is heated from 10 °C to 60 °C. The temperature rise is 60 - 10 = 50 °C.
Step 1 - energy required. Q = 150 x 4.186 x 50 = 31,395 kJ, which is about 31.4 megajoules.
Step 2 - convert to kWh. One kWh is 3600 kJ, so 31,395 / 3600 = about 8.7 kWh.
Step 3 - heating time. Assume a constant useful input of 3 kW to the water, with heat losses ignored. This supplies 3 kJ each second. Time = energy / power = 31,395 / 3 = 10,465 seconds, which is about 174 minutes, or roughly 2 hours 54 minutes.
Takeaway. Energy rises with water mass and temperature rise. Dividing by a constant useful heat input gives the ideal heating time. Real selection also accounts for heat loss, the cylinder’s own thermal mass, control operation and changing exchanger duty. A greater average useful input completes the same heating task faster; compare the actual manufacturer recovery data.