![]() 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.
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