## Statistical Physics, Volume 5Elementary college physics course for students majoring in science and engineering. |

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Page 93

2.8 Computation of the dispersion Use the general properties of mean values to

show that the dispersion of u can be calculated by the general relation (Au)?=(u –

u)} = u2 – 12. (i) The last

2.8 Computation of the dispersion Use the general properties of mean values to

show that the dispersion of u can be calculated by the general relation (Au)?=(u –

u)} = u2 – 12. (i) The last

**expression**on the right provides a simple method for ...Page 183

(b) By simply averaging, derive an

mean energy E of a particle. Use the symmetry requirement that K.3 = K,2 = K2

when the gas is in equilibrium. (c) Hence show that the mean pressure p exerted

...

(b) By simply averaging, derive an

**expression**for the mean force F in terms of themean energy E of a particle. Use the symmetry requirement that K.3 = K,2 = K2

when the gas is in equilibrium. (c) Hence show that the mean pressure p exerted

...

Page 189

Use this result and the definition 8 = 0 ln Q/0E to derive a relation

energy E as a function of the absolute temperature T = (kB)-1. Compare your

result with the

energy ...

Use this result and the definition 8 = 0 ln Q/0E to derive a relation

**expressing**theenergy E as a function of the absolute temperature T = (kB)-1. Compare your

result with the

**expression**for E(T) derived in Sec. 4.7. 4.29 Dependence ofenergy ...

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### Contents

Characteristic Features of Macroscopic Systems | 1 |

A I | 2 |

I | 6 |

Copyright | |

26 other sections not shown

### Common terms and phrases

absolute temperature absorbed accessible approximation assume atoms average Avogadro's calculate classical collision Consider constant container corresponding cules denote discussion distribution ensemble entropy equal equilibrium situation equipartition theorem example exchange energy expression external parameters fluctuations function given heat capacity heat Q heat reservoir Hence ideal gas initial internal energy interval isolated system kinetic energy large number left half liquid ln Q macroscopic parameters macroscopic system macrostate magnetic field magnetic moment magnitude mass mean energy mean number mean pressure mean value measured mechanics mole molecular momentum number of molecules occur oscillator particle particular partition phase space piston position possible values Prob quantity quantum numbers quasi-static random relation result simply solid specific heat spin system statistical statistical ensemble statistically independent Suppose thermal contact thermal interaction thermally insulated thermometer tion total energy total magnetic total number unit volume velocity