When you use an electrical appliance, most of the electricity used is turned into heat. Will the energy cost of using something like an iron be subtracted from the heating bill making it effectively free? It doesn't seem right but I would think the heating wouldn't have to 'work as hard' and as your appliance cools down the heat is eventually distributed throughout your house.
This is assuming you have electric heating.
They do reduce the heating bill, but.. Let's see some numbers.
The average power consumption of (i) a fridge is 50-100 W, (ii) a television is 50 W, (iii) a laptop is 50-100 W etc. Average power consumption of my household was in the order of 200 W which equals to about 150 kWh per month. Double those numbers and it is still nowhere near enough what an average household needs for heating. Not to mention the appliances are usually not in the same room but rather distributed around the house. While on the topic, I will just mention here that an average person outputs about 50-100 W of heat power, which you can easily verify from the average daily energy consumption of a person which is about 2000-3000 kCal (1 kCal = 4184 J and 1 W = 1 J/s).
The recommended heating power is around 60-70 W/m2 for mild climates and 70-85 W/m2 for cold climates. For a room of 20 m2 (an average-sized living room), you need from 1200 W to 1700 W of heating power. Not to mention there are other rooms in a house which also need heating.
I had a crypto miner briefly which was drawing about 1200 W, most of it converted to heat. In my living room I did not need to turn on the heating. But it does not mean I was saving money in the end, because my heating system was based on gas which is in general (much) cheaper than resistive heaters (electricity) per kWh of heat. How much is the gas cheaper than electricity? It very much depends on the country, but in my experience it ranges from 2 to 5 times. See related discussion on crypto miners and heating: Does bitcoin miner heat as much as a heater
Note that (new) fancy air conditioning systems based on heat pumps are comparable to gas (or even better in some countries!) when it comes to operation cost, i.e. they give more heat power than they consume electricity. How? They take heat from the outside air no matter how cold it is - in reality, they work down to about -10 C.
To conclude - yes, the appliances are reducing the heating bill during a cold season, but not by much! And when you take into account that you have to cool down more during a summer season due to the same appliances producing unwanted heat, in best case the operation costs average out to zero throughout the year.
Thanks to Marco Gulin for his excellent answer. In facility engineering practice, the Transamerica Tower in San Francisco began turning off their lighting after hours during one of the energy cost spikes of the 1970s to save on energy costs, and they discovered that their space heating bills increased slightly in proportion. In this case (before heat pumps!) the heating load of the structure was in part supported by the heat dissipation of the overhead lighting system- in a measurable way.
I do not know what sort of lighting they were using, or whether the skyscraper was heated with gas or electricity.
Yes, using an iron is effectively free in a room that would otherwise be heated by the same electricity input.
"Free" in the sense that the same heat input is being put to two purposes - heating the room and ironing the clothes - and it will cost nothing more than if the iron was off and the room was being heated by a heater to the same level.
I leverage a very similar principle for the heating of our home using a dessicant dehumidifier.
Instead of ventilating the bathroom of hot steamy air after use, and ventilating the place in general, I simply use the dehumidifier to keep the home interior dry.
This recaptures the heat in the steamy air, the drying process itself liberates heat energy from condensing the damp out of the air, and finally the dessicant process is "inefficient" in that it requires some heat input for its cycle (heat that is "wasted").
But the net effect is that I haven't had to put the central heating on this winter. Running the dehumidifier, with all windows shut and vents sealed, is enough to heat the entire premises to a comfortable level, as well as being comfortably dry as opposed to dank.
Obviously, the dehumidifier is not free to run. But it is a small fraction of the price of ordinary electric heating when windows must be open to ventilate damp, and the dehumidifier's "inefficiency" (in that it is not 100% efficient at drying air without outputting heat) is actually part of its 100% efficiency in this application, because it's purpose is not just to dry but also to heat.
It depends on where you live: that is the costs of heating and the cost of electricity. E.g., in France, where 70+% of the electricity is produced by nuclear power stations and the electricity is obscenely cheap, your radiators might be just as electric as any other appliances :)
