Classical Gases: Ideal and Otherwise

2019 ◽  
pp. 81-98
Author(s):  
Robert H. Swendsen
Keyword(s):  
Particle Number ◽  
Second Law Of Thermodynamics ◽  
Ideal Gas ◽  
Second Law ◽  
Interacting Particles ◽  
Entropy Maximum ◽  
General Systems ◽  
Two Systems ◽  
The Ideal

As preparation for the derivation of the entropy for systems with interacting particles, the position and momentum variables are treated simultaneously, in this chapter, for the ideal gas. Releasing a constraint on the exchange of volume between two systems leads to an entropy maximum, just as the release of an energy- or particle-number constraint. This same principle is shown to be true for asymmetric pistons, which allow the total volume to change. The entropy of systems with interacting particles is then derived. The Second Law of Thermodynamics is established for general systems. Finally, the Zeroth Law of Thermodynamics is derived.

Entropy, the magic ruler?

2021 ◽  
Vol 34 (2) ◽  
pp. 227-230
Author(s):  
David Van Den Einde
Keyword(s):  
18Th Century ◽  
Second Law Of Thermodynamics ◽  
Ideal Gas ◽  
Heat Energy ◽  
Second Law ◽  
Cyclical Process ◽  
T1 And T2 ◽  
The Ideal

The 18th century foundations of the second law of thermodynamics are discussed. The association between Carnot efficiency and Clausius entropy is described to show the questionable use of Clausius entropy as proof of Carnot’s assumption that the rate the ideal gas can convert heat energy to work between temperatures T1 and T2 sets a universal limit on the convertibility of heat to work by all 2T cyclical process.

scholarly journals Second law of thermodynamics for batteries with vacuum state

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 408
Author(s):  
Patryk Lipka-Bartosik ◽  
Paweł Mazurek ◽  
Michał Horodecki
Keyword(s):  
Ground State ◽  
Second Law Of Thermodynamics ◽  
Random Variable ◽  
Vacuum State ◽  
Second Law ◽  
Initial State ◽  
Ideal Weight ◽  
Stochastic Thermodynamics ◽  
Unbounded Hamiltonians ◽  
The Ideal

In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.

Energy and heat

2017 ◽  
Author(s):  
Andrew Clarke
Keyword(s):  
Thermal Equilibrium ◽  
Growth And Development ◽  
Constant Pressure ◽  
Open Systems ◽  
Second Law Of Thermodynamics ◽  
Ideal Gas ◽  
Second Law ◽  
Total Entropy ◽  
Isothermal Conditions ◽  
System P

Energy is the capacity to do work and heat is the spontaneous flow of energy from one body or system to another through the random movement of atoms or molecules. The entropy of a system determines how much of its internal energy is unavailable for work under isothermal conditions, and the Gibbs energy is the energy available for work under isothermal conditions and constant pressure. The Second Law of Thermodynamics states that for any reaction to proceed spontaneously the total entropy (system plus surroundings) must increase, which is why metabolic processes release heat. All organisms are thermodynamically open systems, exchanging both energy and matter with their surroundings. They can decrease their entropy in growth and development by ensuring a greater increase in the entropy of the environment. For an ideal gas in thermal equilibrium the distribution of energy across the component atoms or molecules is described by the Maxwell-Boltzmann equation. This distribution is fixed by the temperature of the system.

Classical Ensembles: Grand and Otherwise

2019 ◽  
pp. 258-265
Author(s):  
Robert H. Swendsen
Keyword(s):  
Partition Function ◽  
Particle Number ◽  
Canonical Ensemble ◽  
Ideal Gas ◽  
Grand Canonical Ensemble ◽  
Physical Situation ◽  
Canonical Partition Function ◽  
Grand Canonical Partition Function ◽  
Grand Canonical ◽  
The Ideal

The chapter introduces the grand canonical ensemble as a means of describing systems that exchange particles with a reservoir. The grand canonical partition function is defined in general and calculated for the ideal gas in particular. Other ensembles are described and their relationship to the grand canonical ensemble is shown. The physical situation described by the grand canonical ensemble is that of a system that can exchange both energy and particles with a reservoir. As usual, we assume that the reservoir is much larger than the system of interest, so that its properties are not signifficantly affected by relatively small changes in its energy or particle number.

The Second Law

2021 ◽  
pp. 49-84
Author(s):  
Daniel V. Schroeder
Keyword(s):  
Simple Model ◽  
Large Scale ◽  
Second Law Of Thermodynamics ◽  
Ideal Gas ◽  
The Other ◽  
Model Systems ◽  
Second Law ◽  
Magnetic Dipoles ◽  
Einstein Model ◽  
Identical Quantum

Why are so many large-scale processes irreversible, happening in one direction but not the other as time passes? This chapter answers that question using three simple model systems: a collection of two-state particles such as flipped coins or elementary magnetic dipoles; the Einstein model of a solid as a collection of identical quantum oscillators; and a monatomic ideal gas such as helium or argon. For each system we learn to calculate the multiplicity: the number of possible microscopic arrangements. Taking the logarithm of the multiplicity gives the entropy. And the laws of probability then imply the second law of thermodynamics: Entropy tends to increase.

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