Entropy (thermodynamics)

"Ludwig Boltzmann... saw further into the nature of matter than any... contemporaries until... he hanged himself in the face of their incomprehension and rejection of his ideas. Entropy, he showed, is a measure of disorder... A solid... has a lower entropy that the liquid into which it melts. A gas... has a higher entropy than the liquid from which it evaporates. ...When a gas expands to fill an enlarged volume, its disorder and therefore its entropy increases even though we keep its temperature the same... [W]e become less confident... [that] a molecule will be found in a given small region. ...Entropy [also] increases as the thermal disorder of a substance becomes more vigorous, with increasing thermal motion of... atoms... [and] as... positional disorder increases... [the] available positions of... atoms."

"Boltzmann...was driven to his death by the inability of scientists... to come to terms with this profoundly simple insight."

"'[E]nergy supplied as heat' appears in the numerator of Clausius' expression, for the greater the energy... as heat, the greater... increase in disorder and therefore... entropy. The... temperature in the denominator fits... this analogy too... for a given supply of heat... [added to] a cool [little thermal motion] object... will introduce a... [relatively large] disturbance, corresponding to a big rise in entropy... [and the same heat added to a] hot [lots of thermal motion] object has relatively little effect, and the increase in entropy is small."

"The statement that entropy never decreases in any natural change is the same as saying... molecular order never increases on its own... Molecules... will not form... spontaneously into the Statue of Liberty. A gas will not collect spontaneously in one corner of a container."