So much that we were taught in schools is wrong. Well, perhaps not technically incorrect, but definitely misleading.
Take entropy, for example. We are taught that entropy is chaos. Entropy is randomness.
Not really.
What entropy really is, is averageness. The more average something is, the higher its entropy. The lower energy a system has, the higher its entropy. The fewer states something has, the greater its entropy.
Temperature itself is a measure of disorder. Higher temperature = more energy = more internal motion = greater disorder. Lower temperature = less energy = less internal motion = less disorder.
These concepts are related. Work can only be done when a system has useful differences. Energy flows across gradients, which means the differences have to exist. High entropy systems have low energy gradients.
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