Dating problem cryptography
So, if the surrounding air is 60°, then an 80° pool will shed heat energy twice as fast as a 70° pool.
This is why coffee/tea/soup will be hot for a little while, but tepid for a long time; it cools faster when it’s hotter. Since you lose more heat energy from a hot pool than from a cool pool, the most efficient thing you can do is keep the temperature as low as possible for as long as possible.
This is why the idea of “heat beads” is a useful intuition to use; the same math that describes the random motion of particles also describes how heat spreads through materials.
You can gain a lot of intuition for how heat flows from place to place by imagining it as a bunch of “heat beads”, randomly skittering through matter.This is exactly what your intuition should say about heat: if a place is hotter than the area around it, it will cool off.This is a very long-winded way of saying “think of heat as randomly moving particles, because the math is the same”.: I’m having a debate with my wife that I think you can help us resolve. It has an electric heater, which we set to keep the pool water at 85 degrees Fahrenheit. My wife says we should turn the heater off while we’re away to save energy. The one and only gain from leaving a pool heater on is that it will be warm when you get in.I say that it takes less energy to maintain the pool at 85 while we’re away then to let it drop about ten degrees (summer evenings can get quite cool where we live in upstate New York) and then use the heater to restore 85. And what variables are relevant to the calculation? The same is true of all heaters (pool, car, space, whatever).
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Einstein’s cute trick was to say “Listen, I don’t know what ϕ() is a probability distribution (and the sum of probabilities over all possibilities is 1).