Fun Fact - Body Heat

The Sheliak, a race in Star Trek TNG, seems to have no redeeming qualities whatsoever. They're more than willing to kill all the humans on a planet to make room for themselves. They do have one curiosity though, they live in an environment that is the same temperature as their bodies. Really? Is that even possible? All life, even life as abstract as your computer, requires energy to flow downhill, from an energy source to the outside. In other words, entropy must increase. You accomplish this right now by having an internal temperature of 98.6 degrees, as you burn glucose to think and breathe and beat and digest, and your skin is 84 degrees, and the air around you is 70. Heat flows downhill, from inside to outside, and you're comfortable. If the air were 84, your skin would probably rise to 90, but still heat would conduct and convect away from your body. But what if the air is 98? Now heat can only escape if you overheat, and that's not good. In other words, your body temperature always has to be hotter than the environment. The Sheliak cannot exist as described.

“Wait a minute,” I hear you cry, “some animals on earth seem to do this, at least during the day.” Yes, there is a loophole, but it's gross. If your skin is always wet, or wet most of the time, the water evaporates and pulls heat away. Dogs pant, and humans sweat, and kangaroos (which lack sweat glands) lick special spots on their forearms where blood vessels are concentrated. Evaporation cools the blood as it runs through these vessels, and cools the animal. It's a nifty heat exchanger. But if you're in that environment all the time, day and night, you have to be wet pretty much all the time. Perhaps the Sheliak drink a lot, and sweat a lot. I told you they were a disgusting race. Or perhaps they jump into a stream periodically throughout the day, and even once or twice at night, to keep cool. Either way, they must live near water. This issue is not addressed anywhere in Star Trek. We never even see the Sheliak, so we don't know much about them.

Here's a related question; if you were suddenly wrapped up and insulated, how long would you live? It's not hard to calculate. Let's ignore the heat that escapes as you exhale, for you must surely be allowed to breathe. You're a large enough animal that this heat isn't significant. So all your metabolic heat is trapped. A resting human runs at about 100 watts. I use to put my hand near a hundred watt bulb and think, “This is how much heat I'm putting out right now.” Course the new LED bulbs don't put out nearly that much heat. 1 watt is 1 joule per second, is 0.239 calories per second. A kilocalorie heats a kilogram of water 1 degree. You are perhaps 50 kg, if you're dog gone skinny. It doesn't matter much; more body mass burns more energy, and it's almost the same thing, so a 50 kg person burns 100 watts, a 60 kg person 120 watts, and so on, approximately. It's not really linear, your brain burns a quarter of your energy to do all that thinking, that's a fixed cost, but you get the idea. So let's go forward with our 50 kg example. Each second dumps 0.1 kj = 0.0239 kilocalories into your body. That heats 1 kg of water 0.0239 degrees C. Divide by 50 and it heats you 0.000478 degrees C. 106 F usually causes death. That's a rise of 4.1 degrees C. That happens in 8577 seconds, 2 hours and 22 minutes. You'll probably try to forestall this by panting heavily like a dog, hoping the NCIS agents will find you just in the nick of time, but it's probably best if we don't run the experiment in the first place.

I'm writing this article between exercise sessions, which raises the question, how many watts do I burn when I exercise? I've heard that a long distance runner burns 300 watts over a period of hours, while a power lifter expends 1,500 watts for a couple seconds when lifting his weights. Let's see if this is consistent with my workout.

I go up and down the basement stairs 225 times, taking rests here and there as necessary. It's a kind of stairmaster, but it came with the house, and it doesn't take up any room. The trip up is about 2.5 meters, and I ascend the stairs in 5 seconds. Energy is force times distance, or mass times gravity times distance. A doctor weighed me a couple years ago at 199 pounds, and I swore I'd never weigh myself again, so I can tell everyone I am under 200 pounds. Let's just call it 95 kg. Gravity is 9.8 m/s2, so the work done is 9.8 * 95 * 2.5 = 2327 joules. Divide by 5 and get 465 watts. Course there is the downstroke, which is an easy walk. Call it 120 watts, just a bit more than baseline. So average it out, and yes, it's about 300 watts. More perhaps, because there's waste heat. No engine runs with perfect efficiency. By the time I'm done I'm pretty hot and sweaty, and my wife usually waves me towards the shower; do not pass go, do not collect $200.