While I think I have somewhat an understanding of Entropy. (A measurement of a given state by its tendency proceed to it's most "probable" state), I have somewhat of a problem reconciling it with temperature. Specifically why: dS = dQ / T rearranging the equation a bit... 1/T = dS/dQ, which appears to me that to indicate that at smaller temperature, it is "easier" to increase the entropy of a system. Easier in this case means requires less energy. Am I correct in this assumption? Now, anticipating a bit, suppose this was qualitatively true, why the directly inverse relation 1/T, why not 1/T^2, or e^(-T). Also, supposing this were to be true, is there any quantitative usefulness to this? That is what sort of phenomenas can we predict defining Entropy this way. Is Entropy conserved? What sort of useful properties does it have?