Yes I know we’re moving into Spring now but I am wondering,
If I switch all the light bulbs in my house from incandescent to fluorescent, next winter is my heating system going to have to work a bit harder to make up for the loss of heat that the incandescents previously provided?
If I had a heating system that cost more to run per btu than electricity, I might be paying more.
Of course in the summer I’d make out on my central AC not having to get rid of the heat from incandescents.
Yup, resistance heat is ~100% efficient at converting electric power to heat, so you’re basically losing the wattage of the [(incandescent bub minus the fluorescent bulb) x number of bulbs], in heat, during winter. You’re correct that you’re going to be saving money by needing less A/C in the summer.
However:
Usually gas heat is cheaper per Btu than electric, and heat pumps (if you have one of those) have a greater-than-100% efficiency, so it’s unlikely you’re going to be losing money on your total heating + electric bill.
The high positioning of lightbulbs usually makes for poor circulation, so the felt heat of an incandescent bulb will probably be somewhat worse than a standard floor mounted heater + blower.
You can always compensate by leaving your computer on longer, running the toaster more often, or buying a standalone electric heater. All those are going to be 100% efficient heaters as well.
Yes, your heating system will have to turn on more often assuming you keep the same room temperature and have the same heat loss from the house. It’s not quite as simple as getting rid of, say 500W for example, of heat that was coming from the lights that the heating system would now have to replace. The light wasn’t set up to disperse it’s heat to you (or your thermostat) by natural or forced convection like your heating system does so a lot the heat it created didn’t help your heating load. But some of it did make it to your thermostat and keep it from turning on quite so often so it will definitely work at least a bit harder.
(NM, messed up)
IANanelectrician, I’ve only taken one physics class and I failed high school math. The following is my uneducated guess (confidence-inspiring, eh? :D):
To get the same 1750 lumens in a CFL, we’d only need a 24.306W bulb, which gives off 21.63194W of heat.
The difference in heat output between the incandescent and equivalent CFL is 75.76806W.
75.76806W = 258.531352 BTU/hr (or just “BTU” in this context), which is how much lost heat your system will have to make up.
The efficiency of natural gas heating systems range from 55% to 97%; we’ll assume 80% for a typical gas furnace. That means you’ll actually be paying for 323.16419 BTU.
Using sample California gas and electricity rates from PG&E, gas costs $0.90567/therm (100,000 BTU) and electricity costs $0.17643/kWh.
323.16419 BTU costs $0.002926801119573.
75.76806W costs $0.0133677588258.
In other words, it seems like the bulb would cost you 4.6x as much for the same heat output… but I’m not sure if this is the right way to do this calculation.
Serious comment here–all of those extra digits that you are showing in the results of your calculations do not actually add any useful information.
Check out this wikipedia entry on significant figures.
Serious question: I understand what you’re saying, but if I keep rounding with each calculation, doesn’t it get increasingly imprecise? I thought the rounding should only happen at the last step (which was 4.6x for me)?
Reading the section on superfluous precision, it says that 8.53970965 m/s should be reduced to 8.540±0.085 m/s because the original data was “100 m race in 11.71 seconds”… but where did the 0.085 come from?
If you had a heating system like that, you really should get some electric space heaters…
I do seem to recall hearing about office buildings where everyone replaced CRTs with LCD monitors, and found that the heating system was no longer adequate. Though I’m not sure if that was an actual example or just a possibility…
Fair enough comment, but I actually didn’t even notice your final answer buried in the last paragraph. All I saw was the blizzard of figures preceding this.
Back when I was teaching, and wanted to show all of my calculations, I did indeed carry all figures in my calculator until the end, at which point I rounded. However, if you are actually going to show all of your work, you generally round off the intermediate results when you write them down, even if many more digits are being carried through on your calculator. This is because actually writing down results (even intermediate ones) to unrealistic levels of precision is very distracting for someone trying to follow your work.
It has to do with the degree of uncertainty (expressed as a % error) in the original data, which is additional information that may or may not be available. If you don’t know the degree of uncertainty, you are forced to use significant figures rules. This is preferable to expressing results to unrealistic degrees of precision.
See the following paragraph in your link:
Actually, using significant figure rules, I would say that the 100 meters has at least three significant figures (and should therefore properly be written as 100. meters or 1.00 x 10[sup]2[/sup] meters. One could even argue that this figure should have four significant figures, since the track distance is likely precise to at least that amount. However, let’s stick with three significant figures. The race time (11.71 seconds) has four significant figures.
The result of the calculation should therefore be reported to three significant figures (8.54 m/s).
Expressing the result as 8.53970965 m/s is simply incorrect. It implies a far greater degree of precision than is actually the case.