Beer mat physics - the Sun

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Beer mat physics - the Sun

#1  Postby campermon » Jun 04, 2010 2:33 pm

So, I was was sat out in the garden this afternoon, having a beer and constructing my next response to Jerome (formal-debates/formal-debate-existence-of-ghosts-apparitions-t6927.html) when it occurred to me that the opportunity was ripe for some beer mat physics i.e. let's calculate the power of the sun!!

1. So, I placed a cup of water (measured at 0.25 litres) in the shade (under the table) whilst simultaneously monitoring its temperature and sipping a cool refreshing beer.

2. After a short while (10+ minutes) it was noticed that the T had reached a maximum. The time for experiment was now, but unfortunately some clouds had obscured the sun. Not easily set back, I cracked open another beer and monitored the temperature to ensure it remained static whilst observing the sky for a chink in the clouds.

3. When the Sun broke through, I immediately removed the cup from the shade and placed it directly in sunlight. At the same time I began the stopwatch on MrsC's stylish retro CASIO calculator watch.

4. It was observed that whilst in direct sunlight (the Sun was near the Zenith), the T increased by 3oC in 150s.

Calculations

The specific heat of water is approx. 4.2kJ per oC kg, we have 0.25kg of water and the change in T was 3oC.

The energy supplied to the water was;

E = 0.25 x 4200 x 3 = 3150J

The cup was placed in the Sun for 150s so therefore the power recieved;

P = 3150 / 150 = 21W

The cup had an approximate diameter of 0.10m (approx because the kids have destroyed / eaten all the rulers in the house). So therefore the area of water exposed to the sun was;

A = pi x (0.05)2 = 0.00785m2

So, the power per metre2 can be claculated thus;

Power per m2 = 21/0.00785 = 2675 Wm-2

OK....Wiki tells me that the solar constant is about 1.4kWm-2 so I'm out by a factor of about 2, not bad for a bit of beer mat physics.

After all this exertion, I feel that I may have to sit down in the Sun and have a nice cool beer!

:beercheers:
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Re: Beer mat physics - the Sun

#2  Postby Mazille » Jun 04, 2010 2:35 pm

:rofl:

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Re: Beer mat physics - the Sun

#3  Postby jerome » Jun 04, 2010 2:36 pm

That's excellent! :) At this rate if you drink enough and stya home you could get a research grant! :drunk:
Yours sincerely, Jerome -- a threat to reason & science

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Re: Beer mat physics - the Sun

#4  Postby campermon » Jun 04, 2010 2:43 pm

jerome wrote:That's excellent! :) At this rate if you drink enough and stya home you could get a research grant! :drunk:


:thumbup:

I'm thinking of submitting a research proposal to 'Fosters'..!

:cheers:
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Re: Beer mat physics - the Sun

#5  Postby HughMcB » Jun 04, 2010 2:50 pm

Actually that was quite a good result in a somewhat uncontrolled experiment.

Well done, enjoy the beers! :cheers:
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Re: Beer mat physics - the Sun

#6  Postby 100thIdiot » Jun 05, 2010 2:15 pm

Superb, keep up the good work!
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Re: Beer mat physics - the Sun

#7  Postby 95Theses » Jun 05, 2010 2:19 pm

I think that the reason you have overestimated the total power is because you assumed that all the energy was recieved directly through the top of the glass, when you factor in that the air is warmer around the glass itself in the sun and also the reflected sunlight heating the water through the glass that is a surprisingly accurate calculation :cheers:
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Re: Beer mat physics - the Sun

#8  Postby campermon » Jun 05, 2010 3:26 pm

95Theses wrote:I think that the reason you have overestimated the total power is because you assumed that all the energy was recieved directly through the top of the glass, when you factor in that the air is warmer around the glass itself in the sun and also the reflected sunlight heating the water through the glass that is a surprisingly accurate calculation :cheers:


:cheers:

I think the next time I'll insulate the container and encase it in foil in order to reduce conduction through the walls.

I was actually quite surprised at the rate at which the water heated up. Quite a case to have solar panels in the UK!

Anyway, your post got me thinking and I recalculated the area of the cup and water exposed to the sun. I estimated that as well as the top surface, approx half the outer wall of the cup was exposed to direct sunlight.

The cup has an approx height of 0.1m and a diameter of 0.1m so the total area exposed was;

A = 0.00785m2 + (pi x 0.1 x 0.1)/2 = 0.02355m2

Recalculating the power per metre2 gives us;

p = 21 / 0.02355 = 892Wm-2

That's more like it! :smoke:

More 'beer mat physics' to follow in my response to Jerome in the debate thread! :mrgreen:

:thumbup:
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Re: Beer mat physics - the Sun

#9  Postby 95Theses » Jun 05, 2010 3:30 pm

I was thinking about this, do you have a thermos flask? that could be ideal.

And for even greater accuracy you could take a paper cup and paint the inside black to increase absorption and then place it in the thermos!
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Re: Beer mat physics - the Sun

#10  Postby trubble76 » Jun 05, 2010 3:37 pm

You and your science lies! Did you even consider the possibility that the water was heated by a Heater? Intelligent Heating is the only real science here.
To quote jebus; "hot", so you see, it is prophesi profesy foretold.

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Re: Beer mat physics - the Sun

#11  Postby campermon » Jun 05, 2010 4:03 pm

95Theses wrote:I was thinking about this, do you have a thermos flask? that could be ideal.

And for even greater accuracy you could take a paper cup and paint the inside black to increase absorption and then place it in the thermos!


That's an idea.

Something else I have considered is sinking a container into the ground to effectively insulate it.

:thumbup:
Last edited by campermon on Jun 05, 2010 4:05 pm, edited 1 time in total.
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Re: Beer mat physics - the Sun

#12  Postby campermon » Jun 05, 2010 4:05 pm

trubble76 wrote:You and your science lies! Did you even consider the possibility that the water was heated by a Heater? Intelligent Heating is the only real science here.
To quote jebus; "hot", so you see, it is prophesi profesy foretold.

Bloody heretics :naughty2:


:rofl:
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Re: Beer mat physics - the Sun

#13  Postby Sityl » Jun 05, 2010 6:05 pm

I'd like to ask: Does wikipedia's figure talk about energy only at the sun's height in the sky, or in general throughout the day?

If it's the later, than 100% increase may not be unexpected, especially since the sun is at it's highest point for a much shorter time than it is at obscured angles, and for 100% of your experiment's time, it was at the highest point.
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Re: Beer mat physics - the Sun

#15  Postby campermon » Jun 05, 2010 7:03 pm

Jakov wrote:repeat your experiment to get some idea of the uncertainty.


Without fail, as soon as we get another sunny day I'll be sure to be out in the garden drinking beer making precise observations!

:beercheers:
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Re: Beer mat physics - the Sun

#16  Postby campermon » Jun 05, 2010 7:15 pm

num1cubfn wrote:I'd like to ask: Does wikipedia's figure talk about energy only at the sun's height in the sky, or in general throughout the day?

If it's the later, than 100% increase may not be unexpected, especially since the sun is at it's highest point for a much shorter time than it is at obscured angles, and for 100% of your experiment's time, it was at the highest point.


The figure from wiki is based on;

"The solar constant, a measure of flux, is the amount of incoming solar electromagnetic radiation per unit area that would be incident on a plane perpendicular to the rays, at a distance of one astronomical unit (AU) (roughly the mean distance from the Sun to the Earth). " So this would be the flux when directly exposed to sunlight with the sun directly overhead.
http://en.wikipedia.org/wiki/Sunlight

The figure of is derived from satellite data to be 1.366 kilowatts per square meter and so at ground level we'd expect the power received to be smaller (somewhere in my brain I get the figure of 1000Wm-2 at the equator, but I can't remember what source it comes from!). Also, the angle at which rays hit the Earth will be a factor, therefore latitude will be a factor if we are to do the experiment properly.

I think you may also find a value for the average flux experienced on the planet in the wiki (I seem to recall it being several hundred Wm-2).

:thumbup:

edit to add wiki link and further edited for clarity :doh:
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Re: Beer mat physics - the Sun

#17  Postby newolder » Jun 07, 2010 2:19 am

campermon: he is patient.
:cheers:

If the Solar flux is as your first guess suggests, could I bbq a trout with a sheet of aluminium, before dark?
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Re: Beer mat physics - the Sun

#18  Postby 100thIdiot » Jun 14, 2010 2:19 pm

newolder wrote:

If the Solar flux is as your first guess suggests, could I bbq a trout with a sheet of aluminium, before dark?



You could if you emigrated to Thailand, and in only 10 minutes:
http://www.intechnews.com/2008/04/22/cr ... earth-day/
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