How are we hotter than the sun?

Question

According to the Atom series on BBC television a section of the sun, the same size as a person would not produce as much heat as a person does.
I find this concept difficult to understand.

Answer 1

It has to do with thermodynamics. The sun is gas. Humans are more dense. If you take the gas in the suns upper atmosphere, you find that it has a temperature of 5800 degrees Kelvin. But the gas is so thinn that the heat (which is not the same as temperature) in it is not as much as the heat we have in our bodies. The heat in the gas is "diluted". There are so much fewer atoms holding energy than in a human.

Answer 2

First, there is a difference between temperature and heat.
Second, it talked about (so you say) a sun the same size as a person.

I don't think they literally mean a sun that small. I think they would simply mean if one scaled down the size of the sun to the size of a person and scaled down the heat by the same ratio.

The sun has a diameter of about 1.392×10^9 m.

Say a man is about 1.8 m.

The ratio is 7.733 x 10^8.

The sun produces 383×10^24 W

If this is divided by the ratio above the scaled down power would be about 5 x 10^17 watts. That is a lot more than a person can produce.

I don't know what they were trying to say. It is possible you have not told us enough of what was said for us to help you or they may have just been wrong.

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edited

I had another thought on this. If one compares mass rather than size the story is different.

The mass of the sun is 1.9891 ×10^30 kg
The ratio of the mass of the sun to a 82 Kg man (180 lb's) is 2.43 x 10^28.
By that ratio 383×10^24 W would be only 16 milli watts.

That is a tiny amount of power.

Keep in mind that the ratio of mass is a lot bigger than the ratio of size since the mass increases as the cube of a linear dimension.

So this means that person puts out more heat per kg than the sun but less heat per metre then the sun.

Answer 3

There are two concepts here:

heat and temperature.

Heat is an amount of energy.

Temperature is a measure of the speed of the particles that are moving about (and bouncing into each other).

If you move up high enough through Earth's atmosphere, you'll reach a point where the few remaining air molecules are moving about quite rapidly simply because they do not have lots of other molecules to bounce against (and slow them down): the temperature in that area -- the thermosphere -- can reach 2500 C (4500 F). However, if you were floating at that height (approx. 350 km) and stuck your hand out, it would feel c-c-c-cold: there are so few molecules that hardly no energy would flow from the thermosphere to your hand (plus you may feel some pain as the hand would try to bloat because of the near-vacuum -- but that has little to do with the question).

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The sun's energy output is 3.25 x 10^26 W
325,000,000,000,000,000,000,000,000 Watts

That is approximately
77,677,000,000,000,000,000,000,000 Calories per second
(7.77 x 10^22 Calories per second)
with a capital C (the same Calories we use to count the energy content of food).

Over the total area of the sun (6 x 10^18 square metres), that gives us a flow of 12,760 Calories per square metre.

A very active human being, performing a high-energy expending task, could for a few seconds burn the equivalent number of Calories per HOUR (not second).

So the flow of energy (heat) generated by the Sun is far greater than that produced by a human body.

However, if you were to take a "chunk" of the Sun and move it out in space where it would expand to become the size of a person (meaning: it was much smaller than a person when you took the chunk off the Sun), then, maybe, perhaps, this expanding volume of gas would not produce that much heat.

But since I do not know exactly what the BBC actually stated (and even less what they really meant), I too find the comparison difficult to understand.

PS: please redo the calculations just to make sure I did not make a mistake somewhere.

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Output of the Sun:

I used 3.25 x 10^26 Watts
(1 W = 1 Joule per second)
(1 kilocalorie = 1 Calorie = 4184 Joules)

Radius of the Sun
696,270,000 m
Area = 4*pi*R^2 = 6.08 x 10^18 m^2

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Using zebbedee's approach:

A human body's density is close to that of water.
A person weighing 100 kg (on Earth) has a volume of 0.1 cubic metre.

Such a person, if not active, would generate 1800 Calories per day.
That is:
1800 Cal./day * 4184 J/ Cal * 1 day / 86,400 seconds =
87 J/s = 87 W

The human heat generation rate is therefore 870 W per cubic metre.

Answer 4

The suns heat is only generated in the core of the star where the pressure is high enough to sustain thermonuclear fusion. So averaging that over the star reduces the amount of heat production in unit volume. Where heat is the amount of energy output. The suns average density is about 5 Tm^-3 (about the same as granite, even though it is a plasma for the most part). So did the program say the same size or the same mass or the same amount of matter? Taking the average energy output from the small core over the entire star and then a small volume will on average have liitle energy output but with only radiance available to release that energy into space will result in a very high temperature as most of the energy produced will stay within the star. If you could be very efficiently insulated so that very little of the heat you produce could escape so to your temperature would rise. If you didn't die but could just go on producing more and more heat then you could concievably react 1000s of degrees.

It's all in the definitions of heat and temperature.

I get from the numbers above that the suns output is about 0.27Wm^-3, don't know what the out put of a human is per cubic meter but it could be close or a good bit more.

Say a person is about 1/8th of a cubic meter then they only need produce 2.17 Js^-1 or the energy contained in a typical man weighing 70Kg travelling at 0.9 Kh^-1

Yep checked Raymonds calculations and yes they are spot on but you've used area of the sun and volume of a person which are mutually exclusive for comparison, also was looking for energy output of human and found a table which gives basically sitting on your **** you produce about 70W, and running at about 10 mph gives 1150W, so the program is probably right if it's by volume but way wrong if by surface area (coz you have 1/4 of a million kilometers of energy production leaving the surface).

Answer 5

The sun is basically just a big ball of hydrogen gas. It does not burn as there is no oxygen that would fuel combustion. (If all the sun were burning at once, it would disappear in a matter of seconds and the explosion would probably wipe out many of the planets.) The gas on the outer surface of the sun and quite a bit distance in from the surface would pretty much be like the atmosphere on Earth.

In the center of the sun, however, the pressure caused by the hydrogen gas being pulled in by gravitation produces enough heat to induce thermonuclear fusion, where hydrogen atoms combine to form helium and other heavier elements while releasing lots of energy. The outflowing energy lights up the whole ball of gas we know as the sun and makes it glow with the brilliance we can see way out here on Earth.

When it gets down to it, most of the sun is just inert gas waiting for its turn to get down to the core to participate in the practically everlasting thermonuclear reaction that lights up everything in the solar system. It's not producing any heat, it's just sitting there.

Answer 6

hmmm.. well for example the more energy there is left in a battery the faster the "remote control car" travels.. The amount of heat in such a small section would be nothing (in comparison to the size of the sun) Also the sun is huge, and all the energy is spread out evenly. and a person sized amount would contain merely nothing.

A person howver is its own energy source and has less of an area to spread its heat energy.. so thats why..

well i think so

Answer 7

The human body produces more (heat) energy per unit volume than the sun does. But since the volume of the sun is so much greater than that of a human, the amount of heat energy produced by the sun as a whole is of course much greater.

Answer 8

Given that the sun is a nuclear reactor which converts hydrogen to helium I doubt that our body heat would ever be sufficient to do this.

I assume that the programme was taking a section of the sun and stating that it was now remote from the sun? A highly unlikely hypothesis!

Answer 9

You are confusing "hotter", which implies temperature, and "heat" which is a form of energy.
Of course, we are not hotter than the sun: i.e. our temperature is much lower.
On the other hand, the density of energy production (i.e. heat produced per unit volume) in the sun is actually quite low - lower than in your body. But the sun is so huge that it still adds up to a vast amount of energy produced, which of course then radiates out as the heat and light we experience from the sun.

Answer 10

BBC is probably talking bull.