Why not just use a 37mm gun that's uses smokeless powder.
There's no special reasoning for us to design a 40mm autocannon instead of a 37mm one. My original proposal came from a) looking at the Bofors 40mm cannon and the (more time-appropriate
2-pounder, and b) 40mm being a nice, round number.
(I also just noticed that the 1-pounder apparently used blackpowder).
And yes, I do expect we'll be mostly unable (or unwilling) to mount this 40mm quick-firing gun on a tank. There are several examples of 40mm-autocannon tanks from WW2, but only in an AA configuration; the
Nimród, the
Möbelwagen and the
M19 as a main examples. All of them are having open or lightly armoured turrets; they're all almost 20 tons of weight. And, most importantly, they're all WW2 designs.
We actually have an example of similar weapons mounted on a tank and as an auto-cannon:
Ordnance QF 2-pounder and the
QF 2-pounder naval gun. In comparison, the naval cannon is longer, far faster firing, and, well, an auto-cannon. Sadly, I cannot find the weight of the actual cannon for the AT gun. Judging from the relative weights of the German PAK 36 (450kg) and the vehicle-mounted KwK 36 (apparently about 215kg), both 2-pounders seem to be roughly the same weight.
But, finally, remember that we're talking about WW1 tanks, not WW2 tanks.
And, finally finally, I just remembered something: If we design the 40mm cannon and the tank concurrently, we probably won't be able to mount them on our design anyways. In this case, we're restricted to the machine gun or the 37mm blackpowder cannon for now.