I was discussing with some people on reddit about how rate of change in entropy of earth could be maximised and some of them suggested that simply painting the earth black would do be better than all the complex life processes because (they reasoned):

Follows from the thermodynamic definition. Obviously the act of painting itself isn't very important, but the number of microstates in the radiation ensemble is maximal for the black body, or thermal, spectrum.


Because sunlight has a higher temperature(Use the formula of black-body radiation to calcute the entropy of sunlight in unit volume, and then define the temperature of "photon gas" by dS/dU=1/T, you will find the sunlight's "entropic temperature" is proportional to the temperature in the Wien displacement law. For sun, it is about 5800K). If something is colder than this, the process that sunlight(high temperature) tranfer heat to it(low temperature) will be a kind of entropy increasing, and we all know that painting something black will promote this kind of heat transfer.

I'm unsure what a radiation ensemble or even a photon gas is. Anyway the main question is that are these reasons correct? I don't think the second point makes much sense. What I know is that a perfect blackbody will simply absorb all the radiation that falls on it and then re-emit it and I don't see how this could increase the entropy of the blackbody itself.

  • $\begingroup$ Entropy will increase only until it is radiated back out again. $\endgroup$ – Lelouch Oct 31 '16 at 17:28

Anything that results in a net transfer of heat into the Earth will raise the entropy of the Earth. It's true that if you paint the Earth black, it will eventually reach a new equilibrium, and after that there is no further entropy increase, but there is an entropy increase getting to the new equilibrium. This is because less sunlight will be reflected, and that will raise the temperature of Earth, so there must be net heat transfer in.


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