[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 424
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Alexei, you usually ask "why more". You can calculate by knowing the diameter of the Earth, the diameter of the Sun and the distance between them. The diameter of the Sun is much larger than the diameter of the Earth, so no matter how far apart they are, the Sun will "illuminate" more than 50% of the Earth's area. But, this is only one point.
If the calculations show that it illuminates 50.00001%, I see no point in reasoning in this direction.
All the more so because whatever the percentage of illumination is, it does not play any role under the terms of the problem.
The question is how much it got from the sun and how much it lost to radiation in general.
second point - to answer the question you only need to consider ONE day of the planet's rotation. 1000 years will be obtained automatically.
Since the earth radiates into space continuously from all sides and the sun only illuminates it from one side, the only conclusion is that the earth is cooling down, albeit slowly but surely.
In your problem you did not specify the condition of the analysis.
- whether the heat capacity has to be taken into account
- whether the geoprocesses of the core need to be taken into account
- whether the tidal effects of the sun and moon have to be taken into account.
If the problem is reduced to only receiving heat from the sun and releasing it outward, I would say that this process has been stabilized long before the 1000 years of your analysis.
so clarify the factors that need to be taken into account.
As I wrote before - I don't like incomplete TORs.
1. whether the heat capacity has to be taken into account
2. whether the geoprocesses of the core need to be taken into account
3. whether the tidal effects of the sun and moon should be taken into account.
Don't take any of the above into account. Otherwise this problem will never be solved :)
Just the opposite, "otherwise" is the answer is unambiguous)
If we consider only the processes of radiation/absorption of solar energy, and accept that a) during the period in question the inertia of the Earth as a thermodynamic system is constant and b) the Sun has been shining on the Earth even BEFORE the specified thousand years (i.e. was not "turned on" suddenly at moment t=0), then there is no reason to believe that the system is not in thermodynamic equilibrium, so the answer is that the radiated energy is exactly equal to the incident energy.
Don't take any of the above into account. Otherwise this problem will never be solved :)
Hmm. That's interesting.
so the heat capacity should not be considered in the problem. ok. we take it as 0
the intrinsic heat of the planet doesn't need to be taken into account. ok. we take it = 0.
Then give us an example to be sure and the reflection coefficient of the planet =0. that is, everything that comes with sunlight, all goes through the earth. as it has no heat capacity.
Where does that leave us?
that doesn't leave anything.
the earth is a cold black ball, a void.
that's why in physics problems you have to define the conditions of the model. otherwise it'll be like that anecdote
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Three scientists - a mathematician, a zoologist and a physicist - got together to see which horse would come first in a horse race.
They each demanded $10,000 for their research. And after six months, they agreed to meet and tell each other their research.
- The zoologist raised each horse's pedigree to 10 offspring and searched for the best stallions in its bloodline.
- the mathematician studied all the statistics for the last 10 years on races and determined which horse ran better
- and the physicist only managed to create a model of a round horse moving in vacuum. and asked for more money for additional research.
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You wrote down the condition of the problem.
Which is more:
- The amount of energy the Earth took in from the Sun over a period of 1000 years
- or the amount of energy the Earth gave off by radiation into space, over the same period of time? Or are these amounts of energy equal?
- let us then determine where the earth took energy from the sun. in the form of what energy did the earth retain? Your clarification? (you can go back to the heat capacity)
- second point - what will the earth radiate? and where does the radiant energy come from? from the earth itself or from those accumulators that store the sun's energy?
Wow, you've made things so complicated. What a professional programmer means. On the one hand it is of course good, but on the other hand complication does not allow to solve very complex tasks, because they require the opposite - simplification in the beginning and further gradual complication. And you at once. And heat capacity and everything else... Heat capacity, perhaps you should leave it at ..... Let us wait, let others think on this problem too.
I will post a simpler problem later ...
Help me prove the identity my child brought from school. And also explain how to solve, there are a lot of such problems, and I'm something I'm slowing down intensively.
(3*X^2-7*X+2)/(2-6*X)=(2-X)/2