# Heat Up Applications - Energy Required and Heat Transfer Rates

## Energy required when heating up substances

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The energy required when heating 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^{o}C)

dT = temperature difference (^{o}C)

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 at **0* ^{o}C* and heated to **100*^{o}C* (boiling) in one hour. The heat transfer rate can be calculated as*

*q = [( (10 liter) (1 kg/liter) (4.2 kJ/kg ^{o}C) + (2 kg) (0.91 kJ/kg^{o}C) ) ( (100 ^{o}C) - (0 ^{o}C) )] / [(1 h) 3600 (s/h)]*

* = 1.2 kW *

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