Weighing a candle

This is a short movie of a candle being weighed on a precision balance. It is a boring movie, and badly made too. But as Winston Churchill once said:

If a thing is worth doing, it is worth doing badly.

There is one other such movie on You Tube, but well-made though it is – the director clearly used a tripod – I prefer mine.

In fact it is obvious that a candle must be losing weight, and you can make measurements on a much less sensitive scale for a longer time and get a good estimate of the rate at which the cancel is losing weight. But somehow, it is still shocking to see it happen ‘live’.

That’s all.

Candle Mass and Candle Power

Weighing a candle. By determining the rate at which the candle lost mass, I could work out the rate at which it was using up the chemical energy of the wax.

The other day I was looking at a slender candle flame when the thought occurred to me: “How much energy does a candle use to produce that light?“. After a moment of reflection, I thought of two ways to estimate it:

The first method was to weigh a candle as it burned and estimate the mass loss per second. Then I would need to look up the chemical energy of wax per gram (its so-called calorific content) and multiply the two numbers together to get the rate at which energy was released per second.

The second method was to measure the heating power of the candle. To do this I would need to put the candle under a container with a known heat capacity. Then by measuring the rate at which the temperature rose, I could work out the rate at which the candle had delivered energy to the container.

The experimental details are below, but here – for the impatient amongst you – are the results.

• The candle lost mass at a rate of 1.78 mg per second. Multiplying this by what Wikipedia tells me is the calorific value of wax (43,100 joules per gram), I calculate that the candle is consuming chemical energy at a remarkable 77 watts. Wow!
• That’s a lot of power and it is pretty clear that the candle is not producing anywhere near 77 watts of light – I guess the efficiency for producing light must be below 0.1%. Most of the energy must be producing heat.
• I repeated the weighing experiment on a second (nominally identical) candle and I calculated that it consumed chemical energy at a rate of approximately 73 W. Within the uncertainty of measurement, I think this is consistent with the first measurement.
• I used the second candle to heat 250 g of water in a lightweight (105 g) camping saucepan. The rate of temperature rise indicated that the candle was delivering energy at a rate of approximately 44 W.
• So approximately 59% of the chemical energy was being delivered as useful heat. This seems reasonable given my previous experience heating water with flames, and considering that some of the wax may go un-burned (to make the soot in the flame)

So these two quite different experiments seem reasonably consistent, which is pleasing. But the results beg the question: “Could we use that 40 watts of thermal power to produce light more efficiently than a candle can?”.

I asked my colleagues at work – and the answer is most definitely ‘Yes’. You can see a device which does this in action in the movie below, and download instructions on how to make it here.

Experiment#1: Candle Mass

Graph showing the mass loss of candle (in grams) versus time (in seconds). The vertical grid-lines are every 3600 seconds – or one hour. The best-fit to the rate of mass loss is 1.78 milligrams of wax per second.

The rate of mass loss is rather slow. My weighing scale had only 1 g resolution so I needed  to measure for several hours to get a reasonable estimate of the rate of mass loss.

Experiment#2: Heating effect

Graph showing the temperature versus time of 250 g of water in a 105 g aluminium container of candle (in grams) versus time (in seconds). The vertical grid-lines are every 60 seconds – or one minute. The best-fit to the rate of temperature rise is 0.038 °C per second.

This is the raw data of temperature versus time taken using a thermocouple thermometer. I took care to stir the water before taking a measurement.

Time (s)	T (°C)
0	15.2
60	16.9
120	20.2
180	22.6
240	25.3
300	27.6
360	29.5
420	31.1
480	32.9
slope	0.038056	°C/second

I then worked out the heat capacity of the water and the aluminium

Water
	Mass	250	g
	Specific Heat capacity	4.2	J/g/°C
	Heat Capacity	1050	J/°C
Aluminium
	Mass	105	g
	Specific Heat capacity	0.904	J/g/°C
	Heat Capacity	94.92	J/°C
Combined Total Heat Capacity		1144.92	J/°C

Then I multiplied the  heating rate (0.038 °C/s) by the heat capacity (1145 J/°C) to get the rate of energy input (43.6 J/s – or watts).