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The Straight Dope




In your column of August 12, you answered "no" to the question, "does an airplane have a lighter load after the passengers have consumed their food?" Have you forgotten the second law of thermodynamics? Matter cannot be converted into energy and vice versa without some loss. When the airplane passengers eat the food, some of it is broken down in the stomach and used as energy, which is dissipated as body heat through the plane's skin into the surrounding atmosphere. The amount involved may be insignificant--perhaps as little as one billionth of a gram--but yes, the plane does lose weight in flight when the passengers eat food aboard. Looks like the real beanbrain is you, not your reader! --Alex Selkirk, Lompoc, California

Alex, I want you to know that I am filled with Christian love for you, your insufferable personality notwithstanding. Permit me to amend your objection so it makes some sense. The second law of thermodynamics states that, left to themselves, things tend to go to hell in a handbasket. The truth of this assertion is irrefutable, but it has no bearing on the present discussion. What you're thinking of is Einstein's equation E = mc2, which suggests that the extraction of energy from matter (e.g., during digestion) involves some loss of mass.

As you rightly note, however, in this case the amount of loss is insignificant. The average adult human requires about 2,700 kilocalories of energy per day. The potential energy of a kilogram of airline food (or of anything) is 21.5 trillion kilocalories. The loss of mass resulting from digestion is so small that it would fall within the range of error of any conceivable attempt at measurement. What we cannot reliably detect we are entitled to ignore. Ergo, the plane weighs the same after mealtime as before. Go, and trouble me no more.

Pursuant to your column of August 12, I now ask you something a little more challenging. If a passenger on an airplane tosses a baseball into the air, does the plane's weight decrease by the weight of the baseball? I await your amazing answer.

--Hayede Flowers, Los Angeles

That's more like it. The amazing (if predictable) answer is that, although the plane experiences moment-to-moment fluctuations, on average it weighs exactly the same no matter what you do with the baseball, assuming it remains in the airplane. Bearing in mind that every action has an equal and opposite reaction, when you toss the ball upward, you simultaneously force the plane downward, increasing its weight. When the ball becomes airborne, the plane's weight decreases, then it increases again when the ball lands. Having performed various unspeakable rites involving voodoo, human sacrifice, and integral calculus, we find that the average weight of the plane during the tossing process is the same as its resting weight. This demonstrates . . . well, I don't know what, but surely something profound.

But our restless intellectual curiosity won't allow us to leave it at that. (Well, maybe yours will, but I'm in charge here.) Suppose we're carrying a one-pound pigeon instead of a baseball. The pigeon takes off and flies around the cabin. What does the plane weigh? Exactly the same. On average, the pigeon must exert one pound of downward force on the cabin air to keep itself aloft, and the cabin air in turn presses down on the airplane.

Now suppose somebody opens a window. Does the weight of the plane change? Of course, because everybody is sucked out of the cabin and killed. But that's not the point I was trying to make. Let me think. Oh, yes. Antecedent to the loss of payload, the plane still weighs significantly less, if not necessarily a whole pound less, because it's no longer a closed system. Some of the downward force of the air being beat down by the pigeon's wings is dissipated to the exterior darkness. This may not seem like a big deal, and perhaps it isn't, but I have always thought an appreciation of the thermodynamic realities enhances one's quality of life.

Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.

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