Question 1: Why is the earth not in thermal equilibrium with the sun?

ANSWER

The condition for thermal equilibrium is that the two systems must be at the same temperature so that there is no net heat flow between them. As the temperature of the sun is very high as compared to the temperature of the earth, therefore, there is a net flow of heat from the sun to the earth. But the radiation reaches from the sun to the earth is not sufficient to increase the temperature of the earth to such a high value which is comparable to that of the sun.

(1) Earth is spherical in shape, therefore, at any instant of time, only half of the earth is receiving light radiations form the sun. Part of these radiations is absorbed in the atmosphere. Moreover, due the shape of the earth, most part of the light from the sun does not fall normally on the earth surface.
(2) Earth radiates part of the heat back to the atmosphere and outer space which significantly decreases the temperature of the earth.
So, due to these reasons, earth is not in thermal equilibrium with the sun.