## Domestic Energy – understanding the numbers

This blog post is designed to help you (and me!) understand the numbers related to assessing energy use. It is a kind of domestic energy values primer.

## Power and Energy

In general conversation the terms ‘Power’ and ‘Energy’ are often used interchangeably, most confusing, as each has its place.

**Power** is energy is used over a period of time, and that ‘**’energy**“ is measured in watts. This is the international standard (SI) unit and is named after the Scottish engineer James Watt (1736–1819) who was the inventor of the steam engine. A watt measures the unit rate of energy conversion and is defined as one joule per second.

What (!) does this mean in the real word? If you know someone who is a bit on the large side then they may weigh about 16 of your British stones (100kg/ 220lbs). If that person goes up a normal domestic staircase (say 3 m vertical) in ten seconds (which is relatively slowly) then they will be ‘working’ at a rate of around 300 watts. That’s the same as switching on three or four normal incandescent light bulbs.

A single watt, therefore, is a bit on the small side for measuring whole house power consumption and we use the kilowatt instead (abbreviated to kw). That’s one thousand watts. If you are still struggling to get a feel for this then one kilowatt is about one and a third horsepower. So, roughly speaking, a small 75hp car uses 100kw. It takes the power of 1,000 light bulbs to accelerate such a family car crisply. No wonder battery powered electric cars struggle.

Power, then, is what is measured by your domestic electricity meter, and is measured in units of energy (watts) used in a given time, that is kilowatt hours (kwh). For gas consumption the measurement is indirect as your gas meter measures the volume of gas your dwelling consumes and that is converted to power by the declared ‘calorific value’ of the gas. This gives the power delivered for each cubic metre of gas.

## Where does that power go?

Let’s consider space heating, as that is by far the largest consumer of power.

When the building is being heated the temperature of the inside is being kept artificially higher than the external air. Heat passes from the warm house to the outside at a rate that is dependent upon…

- The temperature difference
- The ‘leakiness’ of the walls and windows
- The rate of air change (draughtiness)

### Energy lost through temperature difference

The heating power used is directly dependent upon the temperature difference. So, if the inside is being held at a constant 20^{o}C , then the building will lose twice as much power when the outside is at 0^{o}C (20^{o} difference) compared to being at 10^{o}C (10^{o}) difference.

Hence the argument that you will save a lot of money if you turn down the thermostat by 1^{o}C. With typical temperature differences being in the range of 10 to 12 degrees than a simple calculation shows that you could save up to 10% of your energy bill for space heating. However, as we will see, there are far bigger gains to be made elsewhere. But in the meantime grab a jumper and turn it down a bit.

### Energy lost through walls, windows, doors, floors and the roof

Similarly, if a wall is insulated twice as well as another then the rate of energy loss will be halved. This insulation value can be measured as a ‘U-value’ and is expressed in watts/m^{2}/^{o}C. That is energy lost per square metre of surface per degree Centigrade. You can find tables giving the U values for common building materials that can be used to calculate the rate of heat loss.

There’s a lot more science to this if you want to get into calculating the heat loss of complex builds. E.g. a timber framed wall can have a thickness of plasterboard, one or two types of insulation plus and external cladding. If you are going for a new build and heading for one of the top insulation standards then you either need to master this or find some software to help. For us mere mortals who are seeking to make improvements to existing then standard tables are close enough as we are seeking to make improvements of two or three times to current values.

### Energy loss through air change

The air contained in a building must be replaced over time. We all breathe, so the carbon dioxide must be flushed and replaced with more oxygen, water vapour given off from washing and cooking must be removed to prevent condensation, odours and noxious materials (burnt food/ paint) must be removed and replaced with fresh air.

If a building were sealed it would not be long before it felt very stuffy. In the opposite case the building feels draughty and uncomfortable on cold days.

Any air change involves heating up the incoming air to the room temperature and the energy to do this can contribute up to 30% of space heating requirements if the process is not managed.

So let’s try some maths – well arithmetic really – it’s not difficult.

The energy required to heat up air is calculated from its Volumetric Heat Capacity. For air we can take it as 0.001297 Joules per cubic cm per ^{o}C, that is 1,297 Joules per cubic metre.

A typical domestic room may have a floor area of 3m by 4m and a height of 2.5m. That makes 30 cubic metres of air. For a three bedroom dwelling there would be typically eight such spaces giving a building volume of 240 cubic metres. If we take a fairly typical domestic air change rate of three to four per hour then the volume of air to be heated becomes, say, 800 cubic metres per hour.

On a typical spring day the outside temperature may be 10^{o}C and the internal temperature at a comfortable 20^{o}C, i.e. a 10^{o}C temperature difference.

So the energy requirement is 1,297 * 800 * 10 = 10,376,000 Joules per hour

Now a watt is a Joule per second, and there are 3,600 seconds in an hour (60 * 60).

So the energy requirement is 2.88 kw.

### This is a simplification of the real case

In reality, if you have studied physics at all, you will know that heat transfers not just by conduction, which is what we have been discussing, but also by convection and radiation. However, if the general principles of good management discussed here are followed then the contribution of these methods is relatively small and can be neglected for our, somewhat cavalier, purposes.

## A note about temperature scales

In building calculations and physics you will find reference to degrees Centigrade (C) and degrees Kelvin (K). You can treat these interchangeably as each degree change is identical on both scales. The difference is where the zero is placed. For Centigrade it is at the freezing point of water, for Kelvin it is at absolute zero (-273 and a bit C). However, the calculations we do are all based on temperature difference and so it does not matter which scale you use, just be consistent and use Centigrade as that’s what people use every day.