7. Early in Earth’s history, astronomers hypothesize that the sun’s energy outpu

Question

7. Early in Earth’s history, astronomers hypothesize that the sun’s energy output was 30% less than it is today.
a.Would a faint sun emit radiation at longer or shorter wavelengths than today’s sun?
b.If the energy given off by the faint young sun was 70% of the energy the sun gives off today, how much colder would the earth have been, as a fraction of its current surface temperature? Assume the earth was then, as it is today, in thermal equilibrium. Assume nothing else changed on earth, just the strength of the sun. (Hint: for this calculation you need to know the Stephan-Boltzman equation, which we saw in class, but you don’t need to know the numerical values of any constants in the equation. You only need to know how much less energy the sun was radiating. Show your calculation.
c. Earth’s average surface temperature today is 284K. Given your answer to question b, what was Earth’s surface temperature at the time of the faint young sun? Give your answer both in degrees Kelvin and Celsius.
d. Your answer to question c should be cold enough that there would have been no
liquid water on earth. But, geological evidence shows that there WAS liquid water on earth, even at the time of the faint young sun. Offer a possible resolution to this paradox. Hint: In part b we assumed “nothing else changed”, but that must not be true. What could have changed to allow liquid water on earth even after the suns output dropped like this?

Explanation / Answer

a)We know from the relation E = hc/lamda where h is planck's constant,c is velocity of light and lamda is wavelength of light from the above relation we conclude that the energy is inversely proportional to the wavelength.Hence if wavelength is large than energy is low and if wavelength is small than energy is high. b)we know that E = sigma * T^4 and E1 = 70/100 * sigma * T1^4 or E1/E = 0.7 * (T1/T)^4 or E1 = 0.7 * (T1/T)^4 * E c)substituting T1 = 284 K in equation (1) we get the energy output of sun today d)The presence of liquid water at the time of young sun is true.This is because the liquid water existed in the boiling form that is at 100oC.

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