You make more heat than the Sun

Say what?  The sun’s temperature is surely very much higher than our temperature – in fact, in absolute units, it is nearly 20 times hotter (nearly 5800 Kelvin, in scientific units, while we’re less than 310 Kelvin, or K).  The sun is also considerably bigger than any one of us, or all of us. Its mass is about 330,000 times the mass of our own earth, and the earth’s mass is about 86 sextillion times (86 x 1021) more than our tiny little 70 kg or 154 pounds apiece.  Yet the statement in the title is true in one important sense: the average kilogram of our body generates more metabolic heat than the average kilogram of the sun.

 

One way to get at this figure is that, at rest, we put out about 70 Watts, less than the (fortunately less and less common) 100 W incandescent light bulb.  Still, we’re at 1 watt (W) per kilogram.  We eat to maintain that rate.  Over an hour, that 70 W amounts to an energy use of 70 x 3600 Joules.  Now, a Joule is 0.242 calories and a food calorie (Cal) is 1000 of the standard calories, so in that hour we metabolize about  65 Cal. Over a 24-hour day, we then need 24 x 65 = 1560 Cal…well, more like 2,000 if we’re minimally active or 10,000 if we’re top-notch mountain climbers or skiing across Antarctica.

 

How much power, which is energy per unit time, does the sun put out?  By the time sunlight reaches the surface of the earth, its peak at noon is as high as 1000 Watts on a square meter; that’s a hair-dryer’s worth, for every square meter (a bit bigger than a square yard).  Above our atmosphere, it’s higher, about 1360 W per square meter.  It gets more intense as we get closer to the sun.   You can search a book or the Internet for the inverse-square law to find out how much more intense.  Using the fact that we are, on average, 150 million km (93 million miles) from the sun and the sun’s diameter is close to 1,390,000 km (870,000 miles), we can calculate the intensity at its “surface” (remember, no hard surface – it’s a gas bag).  It’s 46,000 times greater than at our distance, or about 63 million watts per square meter, compared to our 70 Watts per 2 square meters of skin surface.  Let’s go on.  Over its whole surface, the sun radiates energy to space.  That surface area is 4 π times the sun’s radius squared, or 6.07 quintillion square meters (6.07 x 1018).  This is 2.36 trillion square miles, if you’d like old English units, and that’s close to a million times the area of the US.  Multiply this by the output per square meter, to get 382 septillion W (3.82 x 1026).  Divide that by the mass of the sun, which is nearly 2,000,000,000,000,000,000,000,000,000,000 kg (or 2 x 1030 in easier notation).  The sun puts out a measly 0.00019 Watts per kg.  You expend 5,000 times more, on a mass or “weight” basis.

 

This low output from the sun is a good thing, so that the sun does not run out of its nuclear fuel in less than its long life of about 10 billion years.  Other stars are much brighter and burn up much faster, in as little as a few million years.  Compared to the sun, we are profligate in using energy…which we capture from the sun through our crops and pastures.  The plants on earth use only 0.3% of the solar energy reaching us, and we capture as food only several percent of what they capture.  This low capture rate can only be helped a little, and it’s why there can’t be too many more of us.

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