![]() ![]() 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. Since entropy increases logarithmically with the number of microstates, the most probable distribution is therefore the one of greatest entropy.įigure 16.8 The sixteen microstates associated with placing four particles in two boxes are shown. 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 16.8. 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 16.7) 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.Entropy is one of the few quantities in the physical sciences that require a particular direction of time, sometimes called an arrow of time.By the end of this section, you will be able to: ![]() The more positive value of entropy means a reaction is more spontaneous. The SI unit of entropy (S) is Joule per Kelvin. In a spontaneous process, the entropy of the process increases. In an isolated system, for example with non-uniform temperature, heat might irreversibly flow and the temperature becomes more uniform thus increasing the entropy.Įntropy of solids (or particles that are closely packed) is more in comparison to that in gases (in which particles are free to move). Note: Isolated systems spontaneously evolve towards thermodynamic equilibrium which corresponds to maximum entropy. This leaves us with problem (C) as the correct answer after option (A), (B) & (D) are eliminated for being partially correct or completely wrong. ![]() Therefore, we can say that entropy (measurement of disorder in a system) always increases and never decreases. If we place the partition back in its position, the gases will not ‘un-mix’ or in other words, will not return to its initial condition. Now, if we remove the partition that separates these chambers, the gases of both chambers will mix with each other. We assume that both the chambers consist of different gases. For example: Let us consider a system made up of two closed chambers separated by a partition. For this question, we’ll have to use the second law of thermodynamics.Īccording to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time and is constant if and only if all processes are reversible. The amount of entropy is a measure of the molecular disorder, or in other words, randomness of a system. Hint: Entropy is the measure of a systemic thermal energy per unit temperature that is available for doing useful work. ![]()
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