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I am trying to understand how entropy is actually a measure of randomness. The definition for Entropy is --> Entropy, the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system.

I don't understand:

  1. what is ordered molecular motion
  2. why work comes from ordered molecular motion
  3. what is randomness in molecular terms
  4. is entropy applicable to quantum particles
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Heat is the transfer of energy that makes use of random motion (thermal motion). It is due to collision between molecules of bodies with different temperatures. It is random because linear momenta of the molecules are oriented at random, there's no preferred direction.

Work in thermodynamics is defined as in classical physics. $dw=\mathbf{F}d\mathbf{x}$. If you perform work on a system say a gas in a container with a piston above, by putting a weight on top of the piston. This is considered an ordered transfer of energy because the atoms of the weight move all in the same direction (contrary to heat).

Entropy is defined in terms of a variation $dS = q_{rev}/T$, rather than in absolute terms as you're text seems to suggest. When you'll study statistical thermodynamics you will see that entropy can also be defined as

$$S = K_b \ln W$$

where W can be be taken to be a quantitative measure of the disorder of the system. And you will apply this definition to systems composed of quantum particles.

See also https://gioretikto.github.io/chemistry/thermodynamics/heat.html

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