Why card · first principles

Why does a surplus have to go somewhere?

Conservation of energy, applied to a body: what comes in leaves as heat or work, or stays as tissue.

why/energy-balanceDomain · physics of energyNo verdict, no grade · first principles are settled
At rest

The model you brought

"Calories in, calories out. Eat 500 over and you gain a pound a week; eat 500 under and you lose one. The body is a bank account, and the withdrawals are fixed."

Whyborrowed · accounting

The why

A calorie is not a thing in food. It is an amount of energy, and energy is never made or lost. What your body takes in must leave it as heat or as work, or stay as tissue. So a surplus is not a number you eat towards; it is whatever is left after the body has spent what it spends, and the body cannot make it vanish. It can only store it.

The bank-account picture is right about the arithmetic and wrong about the withdrawals. The outgoings are not fixed: eating more raises them, because digesting costs energy, a heavier body spends more, and a fed body tends to move more. So a fixed extra on the plate does not build a fixed extra of tissue for ever. It builds tissue until the outgoings have risen to meet it, and then the level holds. What the law fixes is only the sum.

Whysettled · first principle
stored · tissuerises by exactly in minus outin · what you absorbheat · staying aliveheat · digestingwork · movinga float · the outgoings open as the level risesnothing leavesby any other doorthe level, not the pour, is what the law fixes: in − out = stored
A tank. Food energy pours in at the top. Three pipes leave at the side: the heat of staying alive, the widest; the heat of digesting; the work of moving. The level in the tank is stored tissue, and it rises by exactly what comes in minus what leaves, never by more and never by less. The outflow pipes hang on a float: as the level rises they open a little, so a steady extra pour raises the level to a new mark and then holds it there. To draw: the tank, the three pipes with widths in that order, the float on the surface tied to the pipes.

What it unlocks

  • Why "a 500-calorie surplus" is a target and not a knob: the outgoings move, so the surplus that results is measured on the scale, not chosen on the plate.
  • Why weight gain slows on the same food: the pour is steady, the float has opened.
  • Why the 3,500-calorie rule is a rule of thumb: it assumes the tissue is all fat, and a lean-mass change carries about a fifth of the energy per kilo, so lean people move more weight per calorie than the rule says.
  • Where the muscle question starts: the level rises, but the law says nothing about which tissue. That is the partition, the next card.

The principle in one line

The change in a body's internal energy is the heat it takes in minus the work it does; the textbook writes it ΔE = Q − W, and adds that eating raises the internal energy by chemical potential energy and that repeated overeating is stored as fat. For a body the same line reads: stored = eaten − (heat + work). A food Calorie is the energy that warms a kilogram of water by one degree. Where the heat goes, in a day, the physiology text splits about 70 % to the organs' basic work, 20 % to activity and 10 % to keeping warm; and when people are overfed in a ward, the resting outgoings rise by a couple of hundred calories a day within weeks, which is the float in the picture, measured.

Changed

—No revisions. First principles move rarely; when the reader's picture is wrong, it is the picture that changes, and that is recorded here.