I think everyone answered the theoretical part of this question sufficiently
The heat generated by a computer is going to be identical to a coil-based electric heater.
However.. What has not been touched on is perceived warmth. You may be a bachelor, so this might not matter much to you... But those with wives and girlfriends will know how this works! Assuming you have an identical power draw on both your furnace and mining rigs, I would still say you are very likely going to have to augment with the heater.
A furnace designed to create heat and move air (in theory in an efficient manner) is likely going to "feel" a lot warmer than an mining rig of the same wattage. This is simply due to air movement and distribution throughout the house.
One thing I did was stuff my mining rigs in the furnace room, and open the cold-air return duct so they blow warm air into it. I then set the furnace to just run the fan 24x7, even if the burner (gas here) isn't running. End result was an extremely hot laundry room, and a slightly reduced heating bill. I run around 6kw worth of gear, but honestly have no clue how many BTU my furnace is rated at. I did ponder stuffing mining rigs into the cold air ducting itself (right before the burner intake) - but then realized the fire risk probably wasn't worth it! Note to anyone contemplating this (or running wire through a heating duct) - smoke is the most hazardous part of a household fire, and putting things that burn toxic fumes into your air vent system to ensure all the fumes get quickly distributed throughout the house is an extremely poor idea.
Now, had I designed the house ground-up to be "mining rig heated" then this would be a different story! It's very easy to neglect air distribution and simply focus on the raw math though, and modern HVAC systems are in general very efficient at taking created heat and distributing it to where it's needed. Mining rigs not so much.
I agree completely on the "feel" of heat. Hot air blowing on your face will obviously make you feel warmer more quickly than hot air slowly circulating around the room from a couple of computers 10 feet away.
That said, my wife and I actually get too hot by the time morning runs around with a single 2x5830 rig in our bedroom and the door closed. We've relegated to keeping the door open a bit so some of the heat can escape to the rest of the house. This is with outside temperatures of 35-40F. Below 30F, and we usually have to supplement the rig with the in-wall heater.
Last month's electric + water bill was $292 (of which electric was $260 or so). I figure I'm getting around $125 worth of BTC/month for my current mining, which means the net electric cost was somewhere in the neighborhood of $135, which is darn good for us during the winter. Usually, we break $200 in these winter months without a sweat.
No it isn't. The heat coming from the computer is exactly the same per kWh as from a electric furnace.
For all practical purposes, you are of course correct. However, I seem to recall from highschool some decades ago reading about irreversible deformation and iirc, not all energy was transformed in to heat. I would assume the electromigration taking place in side our chips would fall under that. I suppose its like 0.0000000001% (if that) but just curious if thats correct nonetheless?
I'd be curious to know more about this. Doesn't a statement like that go against the laws of thermodynamics? Or, are we talking molecular changes, so that energy is stored in the form of a new molecular structure in 0.0000001% of the case instead of being released as heat?