5.7 The second and third laws of thermodynamics

The second law of thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, we have identified a very promising candidate: entropy. Processes that involve an increase in entropy of the system (Δ S >0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings , we may reach a significant conclusion regarding the relation between this property and spontaneity. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:

To illustrate this relation, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three possibilities for such a process:

1. The objects are at different temperatures, and heat flows from the hotter to the cooler object. This is always observed to occur spontaneously. Designating the hotter object as the system and invoking the definition of entropy yields the following:
   $\text{Δ}{S}_{\text{sys}}=\frac{\text{−}{q}_{\text{rev}}}{T_{\text{sys}}}\text{and}\text{Δ}{S}_{\text{surr}}=\frac{q_{\text{rev}}}{T_{\text{surr}}}$
   The arithmetic signs of q _rev denote the loss of heat by the system and the gain of heat by the surroundings. Since T _sys > T _surr in this scenario, the magnitude of the entropy change for the surroundings will be greater than that for the system, and so the sum of Δ S _sys and Δ S _surr will yield a positive value for Δ S _univ . This process involves an increase in the entropy of the universe.
2. The objects are at different temperatures, and heat flows from the cooler to the hotter object. This is never observed to occur spontaneously. Again designating the hotter object as the system and invoking the definition of entropy yields the following:
   $\text{Δ}{S}_{\text{sys}}=\frac{q_{\text{rev}}}{T_{\text{sys}}}\text{and}\text{Δ}{S}_{\text{surr}}=\frac{\text{−}{q}_{\text{rev}}}{T_{\text{surr}}}$
   The arithmetic signs of q _rev denote the gain of heat by the system and the loss of heat by the surroundings. The magnitude of the entropy change for the surroundings will again be greater than that for the system, but in this case, the signs of the heat changes will yield a negative value for Δ S _univ . This process involves a decrease in the entropy of the universe.
3. The temperature difference between the objects is infinitesimally small, T _sys ≈ T _surr , and so the heat flow is thermodynamically reversible. See the previous section’s discussion). In this case, the system and surroundings experience entropy changes that are equal in magnitude and therefore sum to yield a value of zero for Δ S _univ . This process involves no change in the entropy of the universe.

These results lead to a profound statement regarding the relation between entropy and spontaneity known as the second law of thermodynamics    : all spontaneous changes cause an increase in the entropy of the universe. A summary of these three relations is provided in [link] .