"The entropy of the universe tends toward a maximum"

These words are a famous quote by Clausius in 1852. They are still true today. We will distinguish between the system and surroundings. While it is possible for the entropy of the system to be negative the sum of the system and surroundings must be positive for all spontaneous processes. Thus, entropy is a state function that defines the direction and magnitude of spontaneous change. We are most interestedin chemical change, but entropy also applied to physical change as well.

The Carnot cycle

The entropy state function is defined by the ratio of heat transferred to the temperature. The physical significance of this definition is that there is a greateramount of heat transferred when there are more energy states. So the entropy is proportional to the number of accessible energy states at a given temperature. How can we show that sufch a definition leads to a state function? One way to demonstrate that a function is a state function is to show that it has a value of zero around a closed loop. Such a cycle was proposed by Carnot. The Carnot cycle establishes that entropy is a state function by showing that the sum of entropy changes around the cycle is zero. Neither the work nor the heat is zero around the cycle. The work and heat are path fucntions as was established previosuly when we considered the First Law.

Standard Entropy of Reaction

Once we have established the entropy function we can use it in exactly the same way that we have used the enthalpy state funtion. We can calculate a standard entropy of reaction by obtaining the difference between the product species multipled the their stoichiometric coefficients minus the reactant species. One important difference is that entropy is an absolute quantity. The entropy is equal to zero at T = 0 K for all perfect crystals. Any small amount of residual entropy that arises from imperfections in crystals is an absolute minimum value of the entropy. Then the entropy is calculate starting from T = 0 K. We will not go into the details of the absolute entropy calculation this course, but we note that tabulated entropies at 298 K are absolute quantities. Recall that enthalpies are not absolute and that we needed to define an arbitrary zero of enthalpy as part of the standard state.