21.12:
Entropy and the Second Law of Thermodynamics
The second law of thermodynamics can be stated via the physical quantity, entropy. It states that in any irreversible process, the universe becomes more disordered.
Consider an ideal gas of 'n' moles undergoing an adiabatic free expansion, which is an irreversible process. Since entropy is a state function, its change during this process can be calculated by considering a reversible process with the same initial and final states.
This reversible process can be approximated to an isothermal expansion.
The total entropy change is found to depend on the ratio of the volumes of the gas before and after the expansion. Here, 'n' is the amount of gas and R, the gas constant.
As the environment exchanges no heat with the gas, its entropy remains constant. Hence, the universe's total entropy has increased.
The condition of each gas molecule, described by its position and velocity, makes up the microstate.
A larger volume of the gas implies more possibilities of these coordinates for each molecule, hence, a more disordered system. Thus, entropy quantifies disorder.
21.12:
Entropy and the Second Law of Thermodynamics
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average kinetic energy of the molecules of the heat reservoir is negligible, there is nevertheless a significant decrease in the entropy of the reservoir because it has many more molecules than the melted ice cube. However, the reservoir's decrease in entropy is still not as significant as the increase in entropy of the ice. Thus the entropy of the universe increases.
The second law of thermodynamics clarifies that the universe's entropy never decreases during any thermodynamic process. When the process is reversible, the change of the entropy is given by ΔS = Q/T. But what happens if the temperature goes to zero kelvin? It turns out the absolute zero temperature is not reachable—at least, not through a finite number of cooling steps. This is a statement of the third law of thermodynamics, whose proof requires quantum mechanics.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 4.7; pages 166–169.