Solar Energy and Green House Effect Question

• TFM
In summary, the actual mean surface temperature of the Earth is 288 K, while the calculated temperature without internal heat sources is 255 K. The difference is due to the greenhouse effect, which can be calculated as a fraction of the energy absorbed from the sun. Using the formula for black body radiation, the difference in radiation from the sun and the greenhouse effect can be determined, resulting in a fraction of 150/240.
TFM

Homework Statement

Negelcting internal heat sources, the surface Temperature of the Earth is calculated to be 255 K. Its actual mean surface Temperature is 288 K. The additional heating results from the greenhouse effect. Regarding this as an internalk heat source, calculate that heat source as a fraction of the energy absorbed from the Sun.

The Attempt at a Solution

I am not sure what I am supposed to do exactly, do I just work out the differnect in Temperature and put it over the final temperature (ie $$\frac{33}{288}$$) or do I need to work out the energy in Joules using equations?

TFM

That sounds right to me. The energy in joules would be very difficult to calculate and would be very large because the mass of the surface of the Earth would be huge.

I think you are supposed to work out how much extra the Earth radiates because it's at 288 K and not at 255K, and divide this by the energy that the Earth gets from the sun.

You can do everything in units of W/m^2.
The heat radiation from the Earth for each square meter is Ct^4. (C an unknown constant)
The intensity of sunlight is 1366 W/m^2 but you can't use that because the sun isn't always directly overhead and it isn't always daytime and there are clouds. You can use an unknown constant for the amount of sunlight received per m^2. (lets call this E)

you know that C(255^4) = E

Would this formula be of any use:

$$(1-A)*L_{sun}\frac{\pi r^2}{4\pi D^2}$$

Where A is the Albedo, r the radius of the Planet, D the distance from the planet to the Sun, $$L_{Sun}$$ is the Sun's Luminoscity.

?

TFM

Is the Equation in the post above required for this question?

TFM

TFM said:
Is the Equation in the post above required for this question?

TFM

I don't think so. You can use the incoming energy of the sun as an unknown constant. there are some simplifications made here, because the albedo does depend on having an atmosphere, as does convection, evaporation etc. Then there's the day-night and seasonal cycles. There is years of work here.

But I think the only thing you need here is the formula for black body radiation.

Does this look right then?

$$I = \sigma T^4$$

where sigma is the Stefan Boltzmann Constant, 5.67*10^-8

$$I_{from sun} = 5.67*10^{-8) * 255^4$$ gives 240

$$I_{from greenhouse} = 5.67*10^{-8) * 288^4$$ gives 390

Would you then:

390-240 = 150

and thus make thge answer: 150/240?

TFM

I think that would be it

1. What is solar energy and how does it work?

Solar energy is the energy that is harnessed from the sun's rays and converted into usable forms of energy such as electricity or heat. This is typically done through the use of solar panels, which contain photovoltaic cells that absorb the sun's rays and convert them into electricity.

2. What is the greenhouse effect and why is it important?

The greenhouse effect is a natural process in which certain gases in the Earth's atmosphere, such as carbon dioxide and methane, trap heat from the sun and prevent it from escaping into space. This helps to keep the Earth's temperature at a habitable level, but when these gases are increased due to human activities, it can lead to global warming and climate change.

3. How does solar energy help reduce greenhouse gas emissions?

Solar energy is a renewable and clean source of energy that does not produce any greenhouse gas emissions. By using solar energy instead of fossil fuels, we can reduce our carbon footprint and decrease the amount of greenhouse gases released into the atmosphere.

4. What are the benefits of using solar energy?

Using solar energy has numerous benefits, including reducing our dependence on fossil fuels, creating local jobs, and helping to mitigate climate change. It is also a sustainable and renewable source of energy, meaning it will not run out like traditional sources of energy.

5. What are the limitations of solar energy?

One of the main limitations of solar energy is that it is not always available, as it relies on the sun's rays. This means that it cannot be used effectively in all areas or during periods of low sunlight. Additionally, the initial cost of installing solar panels can be expensive, although it can be cost-effective in the long run due to lower energy bills.

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