How would you summarize the second Law of Thermodynamics?

Levine puts it rather elegantly:

As some wit has put it: "The first law says you can't win; and the second law says you can't break even." (Physical Chemistry, Levine, pg. 79)

Or, in my own words,

The first law says energy is conserved, and the second law says the change in entropy of the universe is nonnegative.

I like Levine's wording better, honestly.

• The first law of thermodynamics states:

Energy cannot be created nor destroyed. That is, energy is conserved in the universe.

Therefore, you "can't win" - you can't obtain more energy than you put in. It all has to be accounted for (since the universe is so big, it is quasi-closed).

• The Kelvin-Planck statement of the second law of thermodynamics is (Physical Chemistry, Levine, pg. 79):

It is impossible for a system to undergo a cyclic process whose sole effects are the flow of heat into the system from a heat reservoir and the performance of an equivalent amount of work by the system on the surroundings.

In other words, the work output can be no greater than the heat input, i.e. the energy efficiency #e# can never be #100%#:

#e = |w|/(q_H)#, #" "" "0% < e < 100%#

where #w# is the work output from the engine, and #q_H# is the heat input from the hot reservoir into the engine.

Another way of saying it is therefore, "you can't break even!"

Put in yet another way - since some heat input is always lost outwards (towards the cold reservoir in the engine scheme), there is always more heat to give more motion.

Entropy, the amount of energy dispersal, increases with more motion present, so the change in entropy of the universe must be nonnegative.