…and readeth the meter and giveth unto us a very large bill. (Well, the bill got sent by email, but that’s beside the point).

Now, I knew it was going to be costly, what with using electricity to heat a house during a cold winter, but I wasn’t quite expecting the figure at the bottom of the bill. Rushed out to check the meter myself, but no, the man had read it correctly. So I spent the weekend (no, not the whole weekend, just a tiny bit of it, a physicist I may be, but I have better things to do at home) doing some quick calculations on what it does cost to heat things.

Let’s take the hot water supply. The specific heat capacity of water is about 4.2 kilojoules per kilogram per degree Celcius. That is, if you want to raise one litre (kilogram) of water by one degree Celcius, you need to put 4.2 kilojoules into it. (NB 4.2 kilojoules, or kJ, equals 1 kcal (Calorie), that is no co-incidence). Just roughly, I reckon the cold water comes into the tank at about 10 degrees, and gets heated to about 55 (call it 60 for round numbers), that means to heat one litre of water I need 4.2 kJ times 50, or about 200 kJ of energy. Our tank holds 130 litres, so let’s say we use about 100 litres a day, which gives use 20 thousand kJ a day.

Domestic electricity supply is usually billed in units, where one unit is 1 kilowatt hour (the energy you would use if you used a 1 kilowatt power appliance for 1 hour). 1 kilowatt is 1 kJ per second, so 1 kilowatt hour is 3600 kJ. So my 20 thousand kJ for hot water translates to about 5 kwh, or units, roughly speaking. At about 17 cents a unit for hot water, that is 85 cents a day. This of course assumes no heat leaks out of the tank, or the pipes, which obviously isn’t true.

And now for heating the house. We have heat pumps, which we make use of in the day, but at night we use underfloor electric heating to avoid keeping our neighbours (and us) awake with that nasty whining noise the outside units make. And here’s where the impact is. The heating in just one room is about 1.4 kW in power (I know this from watching the meter go round), and if that is on for just three hours a night that is giving another 4 units of electricity. That is just one room. Add it all together and the bill becomes quite understandable. And our house is not all that badly insulated, either.

## Matt Gilbert says:

Hi, I am interested in your working out for your electricity cost/consumption

Can you possibly point me in the right direction on a problem please?

I have a piece of water heating equipment of unknown heat output (capacity.

If i put 60 litres a minute through the unit and the temperature gain across water in/ water out is 5 degrees, can you tell me how to calculate the heat output of the water heater.

There seems to be conflicting info on the net as usual.

thank you,

Matt

## Marcus Wilson says:

One litre = one kilogram, for water (very convenient, no co-incidence) and the specific heat capacity of water is 4200 J /kg /C. That is, to heat one kilogram by one degree celcius requires 4200 joules of energy. To heat 60 kilograms by 5 degrees, requires 60 times 5 times 4200 joules, which is 1 260 000 joules. That’s in a minute (60 seconds), so the total power output is 1260000 joules divided by 60 seconds, or 21000 watts. Twenty kilowatts is a viscious heater (but then 60 litres a minute is a lot of flow – at least domestically). Though energy consumption will depend only on how much you heat, not how quickly you heat it (assuming no energy losses through poorly insulated tanks and pipes, etc)

## Matt Gilbert says:

Thank You!!!!!

You have helped more than you can imagine.

So based onthat, am I over simplifying that you could also work out heat output by heating directly a vessel of known mass (example 100kg of water, raised 40 degrees?). Is it that straightforward?

regards,

Matt

## Marcus Wilson says:

It is that straightforward. That’s how a calorimeter works. (The difficult bit is to make sure no heat ‘escapes’ – but there are clever ways around that.) http://en.wikipedia.org/wiki/Calorimeter

## Matt Gilbert says:

Ok, thank you again. If I’m ever near new zealand I’ll buy you a beer!

best wishes,

Matt