Trying to apply hard-and-fast math to a biological system is like trying to catch a fly with chopsticks - unless you're magic like Mr. Miyagi, it's probably not going to work all that often.
There's a reason that scientists work with large data pools, averages, population statistics, and bell curves, for example. Hank is right on when he mentioned "biological systems" and is talking about how slow and varied the process really is - while all of us have bodies that work pretty much in the same way, there are slight differences within each individual that are going to skew results one way or another. That's why lots of people are needed for study, and why studies are performed over and over and over again to get what we would call "reliable" averages and data. There are individual differences, for example, between myself and Michael, or Michael and Misery, or Misery and Hank that make them all unique systems. Fauna in the digestive tract, eating habits, macros, competency of the digestive system, steroid hormones, past and present medications, etc. that are going to make bodies work differently.
Personally, I've had my weight fluctuate 6 lbs. in a single day. This could be due to many factors - time of day, circadean rhythms of the gut, fluid retention, my hormonal milieu, stress, etc. It certainly didn't mean that I suddenly consumed over dropped 18,000 kcal. (At least, I don't think so, unless I was knocked unconscious and had a lot of food forced down my gullet!)
To answer your original question, you would need plenty of scientific equipment if you really wanted a hard and fast answer, such as a metabolic "cage" (this is an apparatus that is capable of storing and calculating all of your excretions, including sweat, feces, urine, sloughed-off skin, etc.) and they would probably do it over several days.
If you're sincerely interested in digestive/metabolic literature, try scanning PubMed home
--> this is the NIH index of most types of scientific study, organized by keywords. You can search it like you can any search engine. You'll be able to read the "abstracts" (summaries) of any article there, though to read the entire article you'd need a subscription to a journal. Universities and Libraries often have subscriptions, so if you can access pubmed.com through their internet connections, you'll probably be able to get to most of the full article texts.
Female, 31 years old, 5'4 1/2" tall
Starting weight 1/4/11 = 215.2 lbs.
Weight 10/22/14 = 175.0 (net: -40.2)
Last mini-goal: 175 lbs. REACHED 10/22/14 --REWARD: New wallet
Current min-goal: 170 lbs.
Next large goal: 165 lbs. by 12/25/2014
Lowest weight: 156.7 lbs.
150.2 lbs. <--- Official "Healthy BMI" weight
Estimated final goal: 130-140 lbs.
"You don't have to change your life today. You only need to change your day today."