The hot object is comprised of particles A and B and initially contains both energy units. Consider a system consisting of two objects, each containing two particles, and two units of thermal energy (represented as “*”) in Figure 12.8. Conversely, processes that reduce the number of microstates, W f W i, the expansion process involves an increase in entropy (Δ S > 0) and is spontaneous.Ī similar approach may be used to describe the spontaneous flow of heat. 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. In 1865, Clausius named this property entropy ( S) and defined its change for any process as the following: Similar to other thermodynamic properties, this new quantity is a state function, so its change depends only upon the initial and final states of a system. Figure 12.6 (a) Nicholas Léonard Sadi Carnot’s research into steam-powered machinery and (b) Rudolf Clausius’s later study of those findings led to groundbreaking discoveries about spontaneous heat flow processes. 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 12.6) 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.
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