# Thermal Dynamics

Thermal Physics

Deals with a collection of a large number of particles “More is different!” --- P.W. Anderson It is effectively impossible to follow the motion and trajectory of each particle two approaches in thermal physics • Thermodynamics (macroscopic) • Statistical mechanics (microscopic) “Four fundamental pillars of our physical theory: general relativity, quantum mechanics, the theory of elementary particles and statistical mechanics… No single, coherent and clear understanding as to just what the theory of statistical mechanics is or ought to be.” --- Physics and Chance, L. Sklar

Thermodynamics

From the Greek thermos meaning heat (Latin thermae: public baths) and dynamis meaning power Phenomenological theory of matter -- Draws its concepts directly from experiment Macroscopic theory (i.e. it doesn’t contain information about atoms, molecules, …) Does not depend upon microscopic detail (e.g. 1st & 2nd laws, heat flow from “hot” to “cold”, maximum efficiency of engines) Historically, thermodynamics developed out of the need to increase the efficiency of early steam engines

Thermodynamics – widely applied, very fundamental and reliable “Thermodynamics has something to say about everything but does not tell us everything about anything.” --- Goldstein, The Refrigerator and the Universe “A theory is the more impressive the greater simplicity of its premises is, the more different things it relates, and the more extended is its applicability. Therefore the deep impression which classical thermodynamics made upon me; it is the only theory of universal content concerning which convinced that, within the framework of the applicability of its basic concepts, will never be overthrown.” ---Albert Einstein

Statistical Mechanics and Its Relation to Thermodynamics

Mechanics about microscopic physics: classical / quantum mechanics

theoretical Statistical Mechanics

(probabilistic)

Statistics Assumption: each possible microstate has equal probability

Infinite-large limit, i.e. thermodynamic limit

Statistical Mechanics provides an underlying explanation of thermodynamics

Thermodynamics

(deterministic)

phenomenological

Chapter 1 Revision on Thermodynamics

Thermodynamic Systems

heat Q = 0 work W = 0

Isolated system:

Particle number N, energy E are fixed

Q≠0 W ≠0

Closed system:

N fixed E changeable

Q≠0 W ≠0

Open system:

N changeable E changeable

Macroscopic View

Thermodynamics describes macroscopic systems which consist of a large number of small particles (usually of the order of 1023) It is impossible and not useful to keep track of the exact state of motion of all the particles Instead, one describes the system by a few macroscopic quantities that we are interested in

Example: Ideal Gas

Macroscopically, described by volume (V) and pressure (P) Microscopically, it consists of a lot of particles

Each point represents a system

P

V

1.1 The Zeroth Law of Thermodynamics

Thermal Equilibrium and Temperature

Thermal Equilibrium

The idea of temperature is related to thermal equilibrium When two macroscopic systems are in contact, they can exchange different quantities Mechanical equilibrium: Exchange volume → same P Diffusive equilibrium: Exchange particles → same ρ Thermal equilibrium: Exchange energy → same “T” If no exchange is observed ⇔ equilibrium In particular, if no energy exchange ⇔ thermal equilibrium Is this a equilibrium state?

0°C constant gradient 100°C

The time to reach equilibrium ⇔ relaxation time

Zeroth Law of Thermodynamics

If two systems are both in thermal equilibrium with a third system, then the two systems are in thermal equilibrium with each other. --- Ralph H. Fowler, 1920s adiabatic wall (thermally insulating) A C B

Remove the wall, no heat flow

A C B

In thermodynamics, it is an experimental fact Statistical mechanics provides an explanation

Temperature --- A...

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