Do smells have caloric value?

Can you gain calories by spending long hours in a place that has lots of food smell?

For example, a BBQ pit master.

Basically, no.

Calories are produced by fats, proteins, and carbohydrates being digested, i.e. broken into their smallest components, in the intestines.

Scent molecules are not fats, proteins, or carbohydrates. They do not enter the intestines. They are not digested.

And even if they were, their total weight would be negligible. Calories are given per gram of substance. Scent molecules probably don’t add up to more than nanograms.

You’d get more in the way of calories if a random splatter of fat landed on your tongue.

Well, some of it is. I don’t know if fats have an odor, but in any case, if you’re in a kitchen, you’re inhaling at least some vaporized fat. As anyone who’s worked in a ktichen with deep fat fryers knows, fat vapors from the vats condenses everywhere. I’d be willing to bet some carbs and simple proteins get into the air, too.

In addition, if you’re in or near an open distillery you will be inhaling some alcohol along with the still smells (even enough to be dangerous sometimes). And alcohol has calories.

ETA I can attest to this firsthand that this occurs while drinking mulled (and fortified) wine. The combination of the hotness along with the alcohol content made me cough from the alcohol even before I drank any of it!

Sure, but not much. Air masses about 1.3 grams per liter, and any smell component is going to have perhaps 100th to 1000th of that density.
If you breath in 5 liters a minute, that means your nose’ll sample perhaps 0.006 to 0.06 grams of smelly stuff per minute; a max of gram every 15 minutes, if you will.
With continuous smelling, that’d be 96 grams per day. Even if the odor were solid fat, 9 Cal per gram which isn’t likely because long chain (C16 or more) fatty acids don’t have the vapor pressure, you’d only get 864 Calories a day out of it.
Real caloric numbers are likely a factor of a hundred to a thousand times lower.

That sounds like a lot of stuff to inhale. I don’t think a chain smoker inhales that much tar in a day.

I think your particulate molecular mass estimates as a function of air volume are off by a few orders of magnitude. “100ths to 1000ths” should be millionths to billionths at most.

I estimated nanograms, so I agree with this and against Squink’s inflated numbers.

Likely so. I wanted an upper limit, so intentionally kept the estimates high.
I doubt they’d be exceeded even in the case where you spend all day breathing the fumes emitted by heated wine.