This past Winter, one of the ongoing discussions that my housemates and I would have dealt with the amount of money that we were wasting keeping on electric appliances in the house unnecessarily. Everyone knows that keeping the lights on is a waste of money, but exactly how much? At first glance, it seems a simple enough calculation: just multiply the power rating (wattage) by time by cost of electricity and you have a simple answer. However, one factor that would then be missing is the fact that the “wasted” energy of the light bulb goes then to a large extent to heating the house (this is why compact fluorescent bulbs and LEDs are so much more efficient: they don’t generate as much waste heat).
My housemates and I never got around to actually doing the calculations for us in particular, but the question again occurred to me today, so I sat down and did a quick back of the envelope calculation (with extensive use of google and wikipedia). Following:
Cost per Joule of Heat from Electricity
The average residential cost of electricity for 2009 so far is 11.38 cents / kWh (http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_b.html). 1 kWh = 3.6 * 10^6 J. Hence, it costs 3.16111111 * 10^-6 cents / J to heat your house using electricity.
Cost per Joule of Heat from Natural Gas
The average residential cost for natural gas in January 2009 was 12.41 dollars / thousand cubic feet of natural gas (http://tonto.eia.doe.gov/dnav/ng/ng_pri_sum_dcu_nus_m.htm). 1000 ft^3 = 2.83168466 * 10^4 liters.
At STP, 1 mol of gas = 22.4 liters, so 1000 ft^3 = 1264.14494 moles.
Assume that natural gas is 100% methane (not quite true, but close enough).
Heat of combustion for methane: 890 kJ/mol.
Therefore, 1241 cents produces 1125089 kJ of heat
==> 906.598711 kJ / cent
= 906598.711 J / cent
= 1.10302385 * 10^-6 cents / J.
Thus, it costs almost three times as much to heat your house using electricity than natural gas. Of course, this calculation is only partially relevant for such things as light bulbs, Xboxes, computers, etc., because some of the energy is lost (radiation from the house, energy used to send information over wires or the wireless, etc.), but even in the perfectly efficient scenario (which is only likely to occur with space heaters), it’s still considerably cheaper to use natural gas.
