I agree with PhilT (from whom I first heard of this approximation) that 3500 kcal/lb seems a pretty good rule of thumb. It also fits pretty well with our own Tracker results.
I found a paper
here which looks at it in more depth. Pure fat in the body contains energy @ 4280 kcal/lb (39.5 MJ/kg). (Note: adipose tissue - our fat deposits - also include roughly 15% water and 5% protein too.) Protein contains 2130 kcal/lb (19.7 MJ/kg). And weight loss also involves loss of water and (though it is only considered significant in the early stages of weight loss) glycogen.
The protein energy measure needs to be adjusted by a 'protein hydration coefficient' which the writer of the paper estimates at 1.6 g water per g protein, so this reduces the net energy per lb of lost FFM+associated water down to 820 kcal/lb (7.6 MJ/kg).
Assuming this deals with the water issue and ignoring glycogen, that leaves the issue of how much weight we are losing as fat and how much as FFM (in effect, protein+water).
I think it is normally assumed that one loses about 70% fat and 30% FFM, which would on these figures give a weighted average of 3240 kcal/lb. However Dr Michael Mosley has stated (based I think on the ADF studies of Dr Krita Varady) that with IF (including, we hope, 5:2) up to 90% of the weight loss could be fat. This would imply
lower weight loss because fat is a more dense source of energy that FFM: we would need to save 3930 kcal/lb. Neither of these figures are too far away from the 'rule of thumb' 3500 kcal/lb. So I think it is still usable.
josie50 wrote: I found it enlightening to hear confirmed something that I had noticed before: that it's the carbs rather than the fat that makes you overweight
That may be true but not I think for the reason you imagine. It is quite possible to get fat by eating fat or protein, it is just that people tend not to gorge so much on these unless they are combined with carbs especially sugars. That is why having a lot of high GI carbs in the diet is so bad - it encourages feasting and hence taking in too many calories.
The converse is also true: it is quite possible to get thin on a high-carb diet and indeed most successful dieters have done so, and continue to do so. The anti-carb argument is that this is a much harder and (controversially) less healthy way to lose weight than by following a higher-fat calorie-restricted diet.