A couple of people have emailed me on this one, so here is an expansion on the calculation in the SG.
d. A 20 W compact fluorescent lamp uses electricity produced by a coal-fired power station. Use information from Sections 3.2 and 3.3 of the textbook to show that this lamp produces about 160 times more lumen-hours per kilogram of fuel than the candle you considered in parts (a) to (c).
As the SG says, there are several routes but we are looking at light produced per kilogramme of fuel, so let's start from 1kg of coal.
From the information in Box 3.1 of the book, we know that a typical coal contains
- 28 GJ of energy per tonne mass.
- Since 1 GJ is 1000 MJ, and 1 tonne is 1000 kg, we can see then that this means coal contains
- This is 28 MJ energy per kg mass
The overall energy efficiency is (again from Box 3.1) 3.17%. So each kg of coal will produce
- 3.17% x 28 MJ = 0.0317 x 28MJ = 0.888MJ = 888 kJ useful light energy
The SG then converts this to "kWh". This can be confusing because we are used to thinking of kW as a unit of power (which it is - work per unit time). But multiplying it by the number of hours of operations turns it back into a unit of energy, like the joule, but 3600 times larger (because that is the number of seconds in an hour).
So 888 kJ is the same as 0.247 kWh, which the study guide then shows can produce useful light at a rate of 2W for 124 hours - 2W being the rate at which a compact fluorescent lamp whose power consumption overall is 20W produces useful light.
(I've followed the SG approach here, but in fact I personally would have first calculated the electrical energy from the coal and how long that could run the 20W bulb for)
The SG then tells us that this emits about 1400 lumens, meaning that the total light emitted by the lamp from the power from 1 kg of coal is:
- 1400 lumens x 124 hours - 174000 lumen hours.
The kg of candle wax, on the other hand, produced about 1070 lumen hours on burning.
So the ratio of light produced from the electricity from 1 kg coal to the light from directly burning 1 kg candle wax is 174000/1070 = 160.