Why bother buying efficient lights if you are already heating your house? Assume I live in a location where at any time of day and any time of year, I need to heat my house. Assume further that I have a room with no windows. In this case, does it make sense for me to buy efficient light bulbs, considering that any inefficiency in converting electricity to visible light simply leads to more heat being added to the room, which in turn, results in less heat being output by the heater to maintain constant room temperature.
Although these are somewhat idealized conditions, I don't think they are too far off from being realistic. For example, say you live near the arctic circle, it might be smart not to have many windows due to heat loss, and it seems reasonable that in such a climate, heating will be required at all times of the day and year. Assuming I haven't missed something, it seems to me, somewhat unintuitively, that buying efficient light bulbs is not a logical thing to do. Is this the case?
 A: Hot air rises
You'll have noticed the radiators around your house are close to the floor - under it if you're lucky enough. Your lighting, on the other hand, is close to the ceiling. The hot air they produce will do little to warm you where you actually are, usually seated and close to the floor.
A: Heating house with electricity is one of most expensive ways (if not THE most expensive).
Normally houses are heated with coal/oil/firewood/natural gas/heat pumps/RTGs, and only rarely with electric heaters. The electric heating is just more expensive than other sources.
The heat is not "lost", but there are cheaper options to generate it.
Unless your main heating is electrical, replacing bulbs with more energy efficient variants or candles will reduce the electricity bill.
It is also possible you will not want the given room as warm.
It is not likely to happen because of lightbulbs, unless you have a really powerful ones, but I find my room is adequately heated with just my PC running at full load, and sometimes need to be vented to bring temperature down. It's autumn, 10 celsius outside, and the room heaters are off.
A: With more energy efficient lights you can also have brighter ones while still staying within safe watt limits. Less energy used for heat means you can get more light and still not come close to your wiring's tolerance. It's even more important when you have a lighting fixture with it's own maximum wattage. This is due to danger from both the heat generated by the bulb as well as the power draw.
A: The cost of replacing incandescent bulbs is greater than the cost of longer lasting LED lights
The other answers are correct in that:

*

*In many places fossil fuels like natural gas provide cheaper heating than electrical resistance heating (if you ignore the environmental costs), so heating with your lightbulbs will cost you more than your gas furnace.


*The incandescent bulbs heat your house during the times when it is not cold outside and you don't need heat. They also provide an extra burden to air conditioners in the summer.


*Heat pumps are more efficient than electric resistance heating.


*Incandescent bulbs are often not in good locations to deliver the warmth where you need it.
But let's say you live in a perpetually cold place (Antarctica? Mars? A ski chalet used only during the winter?) without cheap natural gas so that (1) and (2) are irrelevant. Let's also assume that you don't have the money to invest in a heat pump, so that (3) is also irrelevant. Let's assume that your house already has electric resistance heating. (4) might be a weak argument, since you usually turn on lights in rooms that you are present and turn them off in unoccupied rooms. LED bulbs still win monetarily.
As you say, for electric resistance heating, all of the input electrical energy is converted to internal energy (the second law of thermodynamics ensures that this eventually happens). Incandescent lightbulbs have much of the same effect, excluding energy lost in light that travels through the windows. Windows are mostly opaque to infrared, which is where most of the incandescent power is going, so losses to radiation out your window are probably small. So if you are constantly heating your house by electrical resistance, what's the difference between heating with your lightbulbs and your purpose-built electrical heater? Electrical heaters can consume a large amount of power for decades, while lightbulbs burn out and have to be replaced.
Here's the thing, LED lights would be cheaper even if they used the same amount of power as comparable incandescent bulbs because they last longer. This website says that you need 1 LED bulb or 21 incandescent lightbulbs for 25,000 hours of use. The 21 incandescent bulbs at \$1 apiece cost your \$21, while the single LED bulb only cost you \$8.
Moreover, you didn't have to change the lightbulb 21 times, which might be an easy task, but it requires some additional cognitive load of remembering you need lightbulbs, buying the lightbulbs, and installing them. Also, using less energy is better for everyone, especially if it comes from nonrenewable sources.
On the large scale, this has been the biggest advantage of LED technology. Municipalities spend a large amount of money just paying people to change high pressure sodium and mercury lamps, so the biggest savings has not come from the energy savings but instead reduced maintenance.
A: From the energy standpoint it does not make any difference, assuming steady state (air convection etc.), in both cases (LED vs bulb) you need P / W for heating the room and reaching the same Lumen.
Example:
heating power needed $P_h$ = 500 W
case 1: $P_{LED}= 20\,W$ for 1400 lm, $\eta = 25$%, Q=4000*20/1000 = 80kWh/year - lifetime 25 years,
P = heating + light 484 W + 15 W = 500 W
case 2: $P_{bulb}= 100\,W$ for 1400 lm, $\eta = 5$%, 400kWh/year, lifetime 1 years,
heating + light 405W + 95 W = 500 W
Lets compare: heater (10hrs/day) + light (10hrs/day) LED vs bulb electricity 0,12 EUR/kWh (best, best case for Europe)
case 1: $484*10*365/1000*0,07$ EUR/kWh + $15*10*365/1000*0,12$ EUR/kWh = 130 EUR
case 2: $405*10*365/1000*0,07$ EUR/kWh + $95*10*365/1000*0,12$ EUR/kWh = 145 EUR
The winner is: LED or at par
BUT with oil/gas you increase additionally your $CO_2$ output much more, regardless whether using green electricity or not. Using a good heat pump COP = 3-4 would be perfect.
A: There's also the generation efficiency that comes into play. In general, about 60% of energy used to produce electricity is lost in conversion, so for every Watt-hour your light bulb consumes more than two Watt-hours worth of fuel have to be burned.
Of course, if you burn these two Watt-hours worth of fuel in your boiler, you'll get almost the full amount as heat: 92-95% for condensing gas boilers and around 85% for traditional ones.
I used the fossil fuel as example, but generation efficiency losses applies to renewable energy as well: e.g. solar panels have efficiency around 20-25%, vs. 60+% for solar water heaters, so 1 electrical Watt-hour is "worth" about 3 thermal Watt-hours.
A: Yes, it does make sense to buy efficient light bulbs in this case. Here is why:
Modern state-of-the-art heating systems use heat pumps to do the heating work. Rather than just "burning" the electricity in resistive heating elements to "make" heat, a heat pump uses electricity to move heat from the outside of the house to the inside- and any waste heat generated in this process is exhausted to the inside of the house along with the heat drawn from outside the house.
This process is inherently much more efficient than using $P=I^2R$ losses to furnish heat.
A: It's highly dependent on where you live and what room you are lighting (Leaving out stuff like gas heating, just looking at electric heating)
According to the 1st law of thermodynamics, energy cannot be created or destroyed. Any "waste" energy from light bulbs is heat, 1:1 as efficient as an electric heater.
However, as one answer already mentions, heat pumps can cheat by "stealing" the heat from the air and are much(up to ~4X) more efficient than resistive heating. However, unless you have a ground-source heat pump(superb, but very expensive and not an option in apartments) or water-source heat pump(need to live by a lake or river), you are looking at air-source heat pumps. They work well in mild climates, but can only work down to ~-4C temperatures(and they are only as efficient as resistive heating at that point.
So if you live at high latitudes(e.g. Edmonton, Alberta, Canada), where the warm part of the year has lots of natural light from the long days anyways and the winter has the long nights you have to light and you only have resistive heating and you are lighting a room with a big south-facing window, then don't worry about the lightbulb efficiency, the aggregate difference will be negligible, but do worry about e.g. the ones in your garage.
Also consider air-conditioning if you have it, even in high-latitude climates with resistive heating, you might still need air-con in the summer if you are in a continental interior. Then, even if a light-bulb, in an interior room with no natural light, is happily heating your house in winter you'll still need it in summer, at which point it's not only using more energy, but also increasing your air-con load.
A: You ask whether "buying efficient light bulbs is not a logical thing to do".
The answer depends on what criteria you apply your logic to, i.e., what you want to maximize or minimize; and then on the circumstances regarding those criteria.
The following criteria come to mind:

*

*Environment

*Economics

*Personal preference and circumstances, e.g. light perception issues, bulb shapes, lighting direction.

The environmental impact depends on the following criteria:

*

*Your climate (is the heat needed?): You mentioned already that you live in a climate where you need to heat most of the time, so there is no additional heat produced when heating with light bulbs.

*How the electricity is produced: In the 1980s in West Berlin electricity was produced together with heat; the efficiency was 80% or better, making it superior to most residential heating. Heating with electricity in Berlin was, as an exception, environmentally benign (apart from its 100% carbon footprint, which it had in common with almost all other energy). Berlin's island status has ceased, however, and today one probably must consider the overall German or even European electricity mix and efficiency which is really not great, unless you like nuclear, coal and gas. But the regenerative fraction is on the rise, and in 20 or 30 years electricity will have a much smaller carbon footprint.

*How you would heat if not through light bulbs: Unless you have low-temperature high-efficiency heating or get your heat from a residential combined heat/electricity power plant like in West Berlin back then, the difference to heating with electricity will be small.

*The environmental cost of bulb production, weighted by bulb life time. Traditional incandescent light bulbs don't contain electronics but just steel, Tungsten and glass which makes them relatively benign. LED bulbs, by contrast, contain electronics which have a traditionally high environmental impact (solder, capacitor fluids, PCB chemicals) and must be treated as special waste. But well-made LED bulbs last decades which I assume outweighs their individual disadvantages.

The economics are in favor of LEDs mostly because they are very long-lasting. Whether the much lower electricity consumption is an economic advantage depends on your heating cost relative to your electricity cost. If you heat with your own wood but generate electricity with a generator you'll be happy; if you have solar cells for electricity but a gas heater you'll not be.
Given that light accounts only for maybe 10% of electricity consumption in US. homes, the economics may be negligible compared to the personally perceived benefits from either choice. Do the dimmable LED bulbs that even change their color temperature (thanks, TCooper) produce the sparkle I get with a halogen bulb at full brightness? Does an LED light at the makeup table reproduce colors faithfully? (But then: What is "faithful"? An incandescent light is typically warmer than daylight, and your office or supermarket will likely have LED or fluorescent lighting anyway.)  On the other hand I replaced a fluorescent light in the kitchen with an LED light. Now the cupboard above it doesn't get warm any longer and I have instantaneous full brightness, two core benefits. I also like LED bulbs in lamps that are frequently moved or touched, like on the desk and nightstand: Vibrations kill incandescent bulbs and some fluorescent lights can break, as opposed to LEDs.
Summing up, the "logical choice" for me is an incandescent light bulb where it fits and an LED light where it fits as well. If in doubt I like LED lights; but my main reason is that the next person to change it will hopefully be my son.
A: You are exactly right in your thinking! However, as others have pointed out even if you live in a place that is cold all the time the heat might not be generated in ideal location (I could put a small heater under my desk to just keep me warm vs a light bulb on the ceiling) and generating heat restively is not as efficient as a heat pump if you have one. But it definitely changes the equation as to whether or not it is worth buying more efficient light bulbs!
Heat pumps are only more efficient when the temperature difference between inside and outside is relatively small. As the temperature outside approaches 0k (maybe you are in Antarctica?) they aren't any more efficient than a purely resistivity heater.
Resistive heaters are by definition the most inefficient appliances known to man. They take nice electrical energy and turn it directly to heat. If hardware price wasn't an issue, it would make a lot more sense to have a 1kw bitcoin miner running under your desk than 1kw heater. At least the bitcoin miner is doing useful work. They both produce 1kw of heat!
For most people, you sometimes have to cool your home so you incur a double penalty. You are wasting energy with inefficient lights, and then you have to use energy to pump this heat out of your home with an air conditioner.
Interestingly if you live in a very cold and damp place using a humidifier can heat your home more efficiently than a purely restive load, because when water changes phase from a gas to a liquid it releases heat. So you end up with whatever heat the motor is generating plus the heat from condensing water.
