The least probable configuration of the system is one in which all four particles are in one box, corresponding to distributions (a) and (e), each with a probability of 1 16. The probability of finding the system in this configuration is 6 16 6 16 or 3 8. The microstates are collected into five distributions-(a), (b), (c), (d), and (e)-based on the numbers of particles in each box.įor this system, the most probable configuration is one of the six microstates associated with distribution (c) where the particles are evenly distributed between the boxes, that is, a configuration of two particles in each box.

The sixteen microstates associated with placing four particles in two boxes are shown. Since entropy increases logarithmically with the number of microstates, the most probable distribution is therefore the one of greatest entropy. The probability that a system will exist with its components in a given distribution is proportional to the number of microstates within the distribution. Microstates with equivalent particle arrangements (not considering individual particle identities) are grouped together and are called distributions. For example, distributing four particles among two boxes will result in 2 4 = 16 different microstates as illustrated in Figure 39.2. The number of microstates possible for such a system is n N. This molecular-scale interpretation of entropy provides a link to the probability that a process will occur as illustrated in the next paragraphs.Ĭonsider the general case of a system comprised of N particles distributed among n boxes. Conversely, processes that reduce the number of microstates, W f < W i, yield a decrease in system entropy, Δ S < 0. Δ S = S f − S i = k ln W f − k ln W i = k ln W f W i Δ S = S f − S i = k ln W f − k ln W i = k ln W f W iįor processes involving an increase in the number of microstates, W f > W i, the entropy of the system increases and Δ S > 0. Note that the idea of a reversible process is a formalism required to support the development of various thermodynamic concepts no real processes are truly reversible, rather they are classified as irreversible. In thermodynamics, a reversible process is one that takes place at such a slow rate that it is always at equilibrium and its direction can be changed (it can be “reversed”) by an infinitesimally small change in some condition. This new property was expressed as the ratio of the reversible heat ( q rev) and the kelvin temperature ( T). A later review of Carnot’s findings by Rudolf Clausius introduced a new thermodynamic property that relates the spontaneous heat flow accompanying a process to the temperature at which the process takes place. In 1824, at the age of 28, Nicolas Léonard Sadi Carnot ( Figure 39.1) published the results of an extensive study regarding the efficiency of steam heat engines. Predict the sign of the entropy change for chemical and physical processes.Explain the relationship between entropy and the number of microstates.We may compute the standard entropy change for a process by using standard entropy values for the reactants and products involved in the process.īy the end of this section, you will be able to: With only one possible microstate, the entropy is zero.

The third law of thermodynamics establishes the zero for entropy as that of a perfect, pure crystalline solid at 0 K.

If Δ S univ < 0, the process is nonspontaneous, and if Δ S univ = 0, the system is at equilibrium.

For a given substance, entropy depends on phase with S solid 0. It may be interpreted as a measure of the dispersal or distribution of matter and/or energy in a system, and it is often described as representing the “disorder” of the system. Entropy ( S) is a state function that can be related to the number of microstates for a system (the number of ways the system can be arranged) and to the ratio of reversible heat to kelvin temperature.

Absolute entropy at 1 atm