Heating Up Applications - Energy Required and Heat Transfer Rates

The energy required to heat up a substance - like a tank, swimming pool or similar - within a certain time can be calculated as

q = m c_p dT / t                     (1)

where

q = mean heat transfer rate (kW)

m = mass of substance (kg)

c_p = specific heat of the substance (kJ/kg ^oC)

dT = temperature difference (^oC)

t = heat up time (s)

Note that heat loss to the surroundings will extend the heat up time. 

Example - Heating up an Aluminum Saucepan filled with Cold Water

An aluminum saucepan with weight 2 kg is filled with 10 liter cold water with temperature 0 ^oC and heated to temperature 100^oC (boiling) in one hour. The heat transfer rate (or required power) can be calculated as

q = (( (10 liter) (1 kg/liter) (4.2 kJ/kg^oC) + (2 kg) (0.91 kJ/kg^oC)) ( (100 ^oC) - (0 ^oC))) / ((1 h) 3600 (s/h))

  =  1.2 kW       

The energy consumed can be calculated as

E = q t                              (2)

where

E = energy (kJ, kWs)

t = time (h)

- or, with values

E = (1.2 kW) (1 h)

   = 1.2 kWh