Ask A Scientist© Environmental Earth Science Archive

name         Susan H.
status       educator
age          40s

Question -   How much coal is required to run a 100 watt light bulb
24 hours a day for one year?
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The missing key piece of information needed here is the energy given off
by the combustion of coal.
Assuming coal is carbon in the form of graphite (not exactly true, but it's
good enough for this type of calculation). That quantity is 3.3 x10^4
kilo-joules / kgm(coal). Using the definition of the watt as:
1 k-watt = 1 k-joule / sec. you only need to calculate the number of seconds
in a year.
     The resulting answer assumes that the conversion of the energy from the
combustion of the coal is converted to electrical energy with 100%
efficiency, which is a huge overestimate. Several factors are not taken into
consideration: 1. The second law of thermodynamics limits the efficiency of
heat into work (which would be necessary if the electricity is generated by
some type of turbine). The efficiency expressed as a fraction, is: (Th -Tc)
/ Th , where Th is the temperature of the combustion of coal, and Tc is the
temperature at which the spent combustion energy is expelled. Assuming Th =
1300 kelvins, and
Tc = 300 kelvins, the efficiency is (1300 - 300)/1300 = 0.77, or 77%. Of
course, this ideal maximum conversion efficiency is never achieved, so a
generous estimate would be 50%. In addition,  the "true" cost is a much more
complicated calculation. The "true" cost takes into account the cost of
mining and transporting the coal, and the operating costs of the generation
(plant cost, salaries, environmental costs, and so on). The bottom line is
that the conversion of coal into electricity is very inefficient.

Vince Calder
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OK.  A 100 watt light bulb uses 100 Joules/sec.  Since a year is 
3.16E7 = 31,600,000 seconds long, 3.16E9 Joules are needed to power 
a 100 watt light bulb for a year.

Bituminous coal provides between 9,500 to 14,000 BTU of heat per pound
when it is burned.  A BTU (British Thermal Unit) is the amount of heat
needed to increase the temperature of one pound of water by 1 degree
fahrenheit.  1 BTU is the same amount of energy as 1054 Joules.  You can
check this (if you want to) by using the fact that a cal increases the
temperature of 1 gram of water by 1 degree Celsius and that 
1 Joule = 4.184 cal.

Using an efficiency of 30% for transforming the heat energy of the coal
into electrical energy and transmitting it to your light bulb (probably
optimistic), we see that one pound of coal provides 4.11E6 Joules to your
light bulb (I take 13,000 BTU/lb x 0.3 efficiency x 1054 Joules/cal).

So finally: 
(energy needed by the light bulb/year)/(energy provided per pound of coal)
 = (3.16E9 Joules/year)/(4.11E6 Joules/pound) = 770 pounds/year.

Since the efficiency is probably less that the 30% I used, you won't be
far off if you say 1,000 pounds of coal are needed to light a 100 watt
bulb for a year.

Incidentally, you may be interested to note that that same amount of
energy would raise the temperature of one million pounds of water through
10 degrees fahrenheit!

Best, Dick...

Richard J. Plano 
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