Thereâ€™s something about the idea of global warming that seems to drive people of a certain mindset completely insane. You start seeing things like: â€œthe planetâ€™s not warming up!â€ â€œOkay, maybe it is warming, but humans couldnâ€™t possibly be causing it.â€ â€œFine. We are causing global warming, but we canâ€™t do anything about it.â€ â€œWhat, we can? Well itâ€™ll destroy our economy.â€ â€œYou mean it wonâ€™t? Well, you must be French.â€

And then you get guyâ€™s like Andrew Longman whose argument runs something like, â€œI donâ€™t believe in global warming, but you do. And congressâ€™s ban on incandescent bulbs is going to put out more CO2 which in your mind means weâ€™re baking the planet. Stupid liberals.â€ Then, after derisively stating that liberals are not hard headed quantitative types, proceeds to lay out an argument that is so stupid, a 12th grade physics class could take it apart.

Unfortunately, a 12th grade physics class isnâ€™t here right now, so weâ€™ll have to do it ourself.

Longmanâ€™s argument is that incandescent bulbs replace some portion of the normal heating used in a house. An NPR story told him that electric heat is more efficient than burning natural gas â€“ in terms of CO2 emissions per unit of heat, therefore, by converting to CF bulbs we are using less electricity to heat our homes and more natural gas therefore, we are putting out more CO2 than if we used the original incandescents. He then proceeds to describe liberals as soft headed and laughs that their silly utopian dreams are undone by lack of an engineering mindset.

Thatâ€™s a challenge thatâ€™s hard to resist. So letâ€™s take this apart. First, Longman doesnâ€™t realize that heâ€™s comparing three different kinds of heating. Heâ€™s simplified to two: gas and electric. But letâ€™s be quantitative and list all three:

- natural gas heaters
- electric resistive heaters
- heat pumps

Natural gas heaters burn natural gas, heating air that is then circulated around the house. Pretty simple idea. Relatively efficient.

Of course, very few people heat their homes with electric resistive heaters. This is the â€œemergencyâ€ or â€œauxiliaryâ€ heat setting on your heat pump. You run electricity through something resistive and generate heat. Itâ€™s a one to one conversion of heat for electricy. Every watt you put in, you get one watt of heat out. Run it for a length of time, and you can covert to watt-hours or BTUs. Now wait, I mentioned that you get electric resistive heaters by running electricity through a resistor â€“ thatâ€™s a light bulb! Okay, we now know that light bulbs are electric resistive.

Itâ€™s very expensive to use electric resistive heat. So most people using electric heat use a heat pump. Think reverse air conditioner â€“ you air condition the outside in winter extracting the heat and putting it into the house. A given heat pump, operating at a given temperature differential will have a specific coefficient of performance (CoP). Essentially, how much electricity does it take to extract a given amount of heat. Depending on circumstances, that CoP may be between 2 and 5. In other words, it takes 1 watt of electricity to extract between 2 and 5 watts of heat from the outdoors and move it inside. Hrm, now weâ€™re starting to see how NPR got its numbers for pounds of CO2 created heating a house with electric vs natural gas.

But of course, Longman has challenged us to be quantitative and so we must preserve persevere. Letâ€™s look at his example. Assume you have a house that contains 30, 100 watt bulbs that are always burning. In his example, a conversion to 20 watt compact fluorescents would mean that instead of getting 3000 watts of heat from the bulbs, you now get only 600 watts of heat from the bulbs and have to burn the equivalent of 2400 watts worth of natural gas. Using his soft, fuzzy, NPR numbers (that heâ€™s misunderstood), Longman says that you emit less CO2 with the incandescents.

But he hasnâ€™t really shown that. So letâ€™s do the math. Basic numbers weâ€™ll need:

- CO2 emissions per unit of heat from natural gas
- CO2 emissions per watt-hour of electricity
- watt-hours consumed using our 30, 100 watt bulbs over a period of time

According to the Natural Gas Association, 1 billion (1,000,000,000) BTUs of heat from natural gas produces 117,000 pounds of CO2.

According to the Department of Energy, we produced 1.341 pounds of CO2 per kilowatt hour of energy generated in 2000. (Note, this is generated, some power is lost in transmission, so this is an upper lower bound for [CO2 generated by] power energy used in a home).

Now weâ€™re getting somewhere. So 30 bulbs at 100 watts each, use 3000 watts of power or 72 kilowatt hours per day. That works out to 96.552 pounds of CO2 per day for heating your home with light bulbs.

What about natural gas? Well, we donâ€™t have a CO2 pounds per kwh for natural gas, but since the CoP of a light bulb is 1.0, we have a conversion from electricity to heat. Our 72 kwh of electricity converted directly to heat turns out to be 245800 BTUs. Which turns out to generate 28.7586 pounds of CO2 if produced by natural gas. Of course, we havenâ€™t replaced100% of our light bulb heat by switching to CF bulbs, only 80%. The other 20% is still [comparable to] electric resistive. So if we take 80% of 28.7586 and add 20% of 96.552, we get 42.311 pounds of CO2 generated by using 30, 20 watt CF bulbs.

Now, unless Iâ€™ve forgotten my basic math, 42.311 pounds is less than half of 96.552 pounds. So, I think that means that Longman was full of crap and is apparently a fuzzy headed conservative and not really a quantitative man at all.

Q.E.D.

**Updated:**

Oh, so I forgot to look at summer when weâ€™re trying to cool the house. Turns out that the difference is even greater. In the summer, all of the heat is waste heat â€“ we donâ€™t want it and we need to get it outside. Assuming weâ€™ve got a high efficiency air conditioner, it takes about one watt-hour of power to remove five watts-hours of heat, i.e., letâ€™s assume a CoP of 5.

In the summer, running Longmanâ€™s 30, 100 watt bulbs 24 hours a day still takes 72 kwh per day plus weâ€™ll need to run the a/c for another 14.4 kwh per day. That gives us a total of 86.4 kwh creating at least 115.824 pounds of CO2.

If we assume that all of those bulbs are now 20 watt compact fluorescents, then we require 14.4 kwh for light, plus another 2.88 kwh for cooling. Total of 17.28 kwh per day for lighting and cooling the lighting. Those 17.28 kwh will createâ€¦ 23.17 pounds of CO2. Or not surprisingly, one fifth the CO2, since the bulbs use one fifth the electricity.

Of course, not everyone is going to use 30, 100 watt bulbs for lighting 24/7, but the relative proportions stay the same.