Which of the following is true about entropy?

a) It is a measure of how spread out thermal energy is within a system. b) The entropy of the universe is at maximum at $\text{0 K}$. c) Entropy always increases in a spontaneous process. d) The total entropy of the universe always decreases.

May 28, 2017

Here are the reasons why $\left(a\right)$ is correct and the rest are not.

$\left(a\right)$ is correct.

The definition of entropy that is generally accepted (or should be, in my opinion) is something like:

The entropy is a measure of the amount of energy dispersal.

In other words, it is a measure of how energy can be distributed throughout a chemical system, which pretty much matches $\left(a\right)$.

$\left(b\right)$ is incorrect, because it's backwards, contradicting the third law of thermodynamics.

From the third law of thermodynamics, the entropy of a perfect crystal at $\text{0 K}$ is zero. Thus, near $\text{0 K}$ it should be near zero $\text{J/K}$, and so, it is "at" its minimum, not maximum.

$\left(c\right)$ is incorrect, because it's too universal of a claim to be true.

Entropy for the system OR surroundings could decrease in a spontaneous process, but either one could also increase in a spontaneous process.

The absolute entropy of the universe, however, always increases.

Spontaneity also depends on the sign, and sometimes the actual value, of the enthalpy for that process at the same conditions, and not just on the sign of the entropy.

For instance, a reaction at high enough temperature with a negative entropy of the system is never spontaneous, but if the temperature was low and the enthalpy was large and negative, then it can be spontaneous.

$\left(d\right)$ is incorrect, because it directly contradicts the second law of thermodynamics:

The total entropy of the universe always increases.