
Contents
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8.1 Thermal Equilibrium 8.1 Thermal Equilibrium
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8.2 What do we Mean by ‘Temperature’? 8.2 What do we Mean by ‘Temperature’?
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8.3 Derivation of the Ideal Gas Law 8.3 Derivation of the Ideal Gas Law
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8.3.1 The Maxwell–Boltzmann Equation 8.3.1 The Maxwell–Boltzmann Equation
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8.3.2 The Pressure in an Ideal Gas 8.3.2 The Pressure in an Ideal Gas
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8.4 Temperature Scales 8.4 Temperature Scales
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8.5 The Pressure and the Entropy 8.5 The Pressure and the Entropy
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8.6 The Temperature and the Entropy 8.6 The Temperature and the Entropy
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8.7 Equilibrium with Asymmetric Pistons, Revisited 8.7 Equilibrium with Asymmetric Pistons, Revisited
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8.8 The Entropy and the Chemical Potential 8.8 The Entropy and the Chemical Potential
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8.9 The Fundamental Relation and Equations of State 8.9 The Fundamental Relation and Equations of State
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8.10 The Differential Form of the Fundamental Relation 8.10 The Differential Form of the Fundamental Relation
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8.11 Thermometers and Pressure Gauges 8.11 Thermometers and Pressure Gauges
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8.12 Reservoirs 8.12 Reservoirs
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8.13 Problems 8.13 Problems
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PROBLEM 8.1 Equilibrium between two systems PROBLEM 8.1 Equilibrium between two systems
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PROBLEM 8.2 Equilibrium between two ideal gases connected by an asymmetric piston PROBLEM 8.2 Equilibrium between two ideal gases connected by an asymmetric piston
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8 Temperature, Pressure, Chemical Potential, and All That
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Published:December 2019
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Abstract
The Maxwell–Boltzmann distribution of momentum is obtained from statistical mechanics. Expressions for the temperature, pressure, and chemical potential are formulated as partial derivatives of the entropy with respect to energy, volume, and particle-number. The temperature scale is derived from comparison with the ideal gas law. The concept of the fundamental relation is defined as an expression that contains all thermodynamic information about the system of interest. Its differential form is introduced. Equations of state contain partial information about the thermal properties of a system and can be expressed as partial derivatives of the fundamental relation. The function of thermometers, pressure gauges, and thermal reservoirs are derived from these principles.
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