Energy and Entropy
Equilibrium to Stationary States
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18 Result(s)
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Book
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Chapter
Applied Boltzmann Statistics
Systems with only two or three possible energies illustrate the Boltzmann distribution. The probabilities for such systems determine average thermodynamic parameters. The intimate connection between the energi...
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Chapter
Maxwell–Boltzmann Distributions
describes a distribution for maximal states consistent with the available energy. If the separation between discrete energies is reduced to a continuum, the Boltzmann factor is proportional to the probability ...
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First Law Formalism
A gas can be characterized by a set of state variables. Some, such as temperature, pressure, and volume, are measured directly in the laboratory. Others, such as internal energy and enthalpy, are determined by...
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Entropy and the Second Law: Thermodynamics Viewpoint
Each reversible step in the cycle gives maximal work but no net work is done for the cycle. All work generated on expansion must be stored and used to return the gas to its initial volume.
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Chapter
Free Energy
The entropy change for an ideal gas is calculated from temperature, pressure, or volume changes. A phase transition occurs reversibly if the system and surroundings temperatures are equal. Entropy is transferr...
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Chemical Potentials in Solution
The vapor pressure for a liquid component changes when it is mixed with other liquids. An ideal mixture obeys Raoult’s law.
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The Foundations of Statistical Thermodynamics
Classical thermodynamics does not require detailed molecular information for thermodynamics parameters. The heat capacity is a proportionality constant relating E to T:
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Multi-state Systems
The number of Boltzmann factors in the partition function increases with increasing energy states. The higher energy states might have small Boltzmann factors but are included for completeness. This leads to i...
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Interactions
A protein with two independent ligand binding sites resolves into two single site partition functions even if the two sites have different binding parameters. The distinct sites can even be on different protei...
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First Law of Thermodynamics: Applications
ΔE is determined from changes in other state variables such as volume and temperature or by measuring the net heat and work transferred across the system boundaries. Since both methods give the same ΔE, they are ...
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Irreversible Thermodynamics and Transport
The product of electrical potential ψ and charge dq is a reversible free energy change Charge is transferred without changing the potential. The energy is the product of an intensive ψ(J/C) and extensive (qC) par...
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The Nature of Entropy
Entropy is different from conserved energies and system variables like T and V that can be measured in the laboratory. However, the product TS has units of energy which suggests that entropy produced in an irreve...
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Thermodynamic Equations of State
An entropy change for the independent variables T and V follows the partial differential path
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Chapter
Phase Equilibria and Colligative Properties
The chemical potential of a system is zero at equilibrium. To maintain equilibrium, a change in T, for example, must be balanced by a change in P, to keep the net chemical potential change equal to zero. For two ...
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Chapter
Statistical Thermodynamics in Chemical Kinetics
The dog-flea model illustrates an equilibrium distribution with the maximal states. If all fleas are on dog A, each might jump to dog B with some characteristic time. Independent jumps by fleas in either direc...
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Chapter
Stationary State Thermodynamics
Classical thermodynamics characterizes macroscopic systems at equilibrium; statistical thermodynamics generates averages of thermodynamic parameters from microscopic molecular information. Irreversible thermod...
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Chapter
The First Law of Thermodynamics
The first law of thermodynamics is the law of conservation of energy; energy is neither created nor destroyed. It can occur in different forms such as thermal or electrical energy and can be converted between ...
