Something must be off with your math. I’ve tested opening a window a crack in my building in montreal. The co2 gets low even with two people present. Heating costs did not double.

Or maybe I had less than ten air changes?

It can’t be that hard to focus on the rooms with people in them, reduce the other rooms to eg one change an hour.

This is already done when calculating ventilation rates. It won't matter much because the majority of space in an occupied building is going to be classified as, well, occupied.

I always wonder how much I save by blocking off the vents in under-occupied rooms. They end up sitting a few degrees cooler in winter.

The problem is very seldom the house. The problem is shared spaces.

10 air changes per hour is a lot; I believe the current recommendations for average climates is 3.

And we're looking at the margins; 1 air change per hour can do wonders for preventing the spread of disease and improving air quality, compared to 0 air changes per hour.

Nevertheless, I redid your math, and found that your hypothetical home has 26,728 more BTUs of energy in its air, compared to the outside air[-1][0][1], and that the recommended furnace for such a climate should be 160,000 BTU/hr [2].

Using those numbers as a base, I find that, with an efficiency of 95%, it would require 120 (that's one hundred and twenty) air changes per hour to double heating costs.

With 60% efficiency, it would require 15 air changes per hour to double heating costs.

And it only takes a few air changes per hour to increase comfort and prevent illness.

[-1] I suddenly realized that the google search links that I used for these calculations are messy and unwieldy, so I'll summarize my calculations: (2600 ft^2) * (8 ft) represent the volume of the house; (1.225 kg / m^3) represents the density of air, (1.005 kJ/(kg * Kelvin)) represents the specific heat of air, (70 * (5/9)) represents the temperature difference you gave me, in Kelvin. Multiplying everything together, and letting Google automatically take care of unit conversions, gives me 28.2 MegaJoules of energy in the house.

[0] https://www.google.com/search?q=%282600+ft%5E2%29*%288+ft%29...

[1] https://www.google.com/search?q=convert+28199142.9+joules+to...

[2] https://www.pickhvac.com/calculator/heating-btu/

My first calculation using entirely imperial units didn't go well... I think I'll stick to metric!

It's unavoidable when discussing residential heating. Just use google for automatic unit conversions, and be grateful that we didn't need to invoke the cumbersome unit of "R-value" to measure insulation!