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# Heating Up Applications - Energy Required and Heat Transfer Rates

## Energy required to heat up a substance.

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 cp dT / t                     (1)

where

q = mean heat transfer rate (kW)

m = mass of substance (kg)

cp = 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 100oC (boiling) in one hour. The heat transfer rate (or required power) can be calculated as

q = [( (10 liter) (1 kg/liter) (4.2 kJ/kgoC) + (2 kg) (0.91 kJ/kgoC) ) ( (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

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

3 10