Units of Measurement

British Thermal Units (Btu), Joules (J) and Kilowatt Hours (kWh)

The above units are measurements of Energy, Work and Quantity of Heat (not to be confused with heat flow).

For those not familiar with metric or SI units, the kWh, in particular, may seem a confusing notation for a measurement only of energy, with the apparent implication that time is involved.

To take an example of the energy required to raise the temperature of a typical 100 litre domestic hot water cylinder.

Energy required is given by mass of water × specific heat capacity of water × temperature rise of water required.

Most quantities of water in the industry are measured in litres, but we require mass; fortunately in metric units the density of water is approximately 1 so the volume of water is approximately equal to its mass.

So if we want to raise 100 litres of water from 4°C to 60°C we require:

100 kilogrammes × 4.18 kilojoules/kilogramme K × temp rise i.e. (60-4) or 56°C = 23,408 Kilojoules.

The approximate equivalent imperial unit calculation:

Again mass × specific heat capacity of water × temperature rise required.

220 pounds × 1 British Thermal Unit per pound °F × 100°F temperature rise = 22,000 Btus.

From the above we can see, as a matter of interest that a Kilojoule approximately equals a British Thermal Unit (Btu).

The Kilojoule may be restated in terms of Kilowatt hours and indeed commonly is for Energy requirements.

As a watt is defined as a joule per second this provides the answer to the conversion between joules and kilowatt hours.

1 kilowatt hour = (1kW)(1 hour) = (1,000 joules per second)(3,600 seconds) = 3.6 million joules or 3,600 kilojoules.

British Thermal Units per hour (Btu/h) and watts (w)

The above units describe heat flow rate or power.

As 1,000 watts equals 1,000 joules per second this is therefore the heat flow rate of a quantity of joules.

Boiler power or air conditioning unit power is commonly quoted in British thermal units per hour or kilowatts, as are other heat sources such as a 3kW fire.

In the example above, therefore, where 100 Kilogram of water was heated by 56°C this required 23,400 kilojoules or 23,400 kilojoules ÷ 3,600 = 6.5 kilowatt hours.

It is simple to imagine an electric heater in a cylinder, and if a heat up time for the cylinder of 1 hour is required, the size of the immersion would be 6.5 kilowatt hours ÷ 1 hour, i.e. 6.5 kilowatts.

If it was acceptable to wait 2 hours for the water to heat up, then an immersion of size 6.5 kilowatt hours ÷ 2 hours = 3.25 kilowatts would be required.

It can be seen from the above how crucial heat up time is to the sizing of equipment.

In the imperial calculation the heater would need to be sized for 22,000 British thermal units per hour for a 1 hour heat up, and half of this, i.e. 11,000 British thermal units, for a 2 hour heat up.