• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Document
Document

Chapter 9 PPT
Chapter 9 PPT

... The time interval during which the velocity changes from its initial to final values is assumed to be short The interaction forces are assumed to be much greater than any external forces present ...
Exercises in Statistical Mechanics ====== [Exercise 0010
Exercises in Statistical Mechanics ====== [Exercise 0010

... (a) Express N̂ using X̂n . Using theorems on adding independent random variables find hN i and Var(N ). (b) Find the probability function f (N ) using combinatorial considerations. Calculate from it hL̂i and V ar(L). (c) Assume |(V /V0 ) − 21 |  1, and treat N as a continuous random variable. Apprx ...
simulating fritz haber`s ammonia synthesis with thermodynamic
simulating fritz haber`s ammonia synthesis with thermodynamic

... Lappeenranta University of Technology • 53851 Lappeenranta, Finland n 1909, Fritz Haber succeeded in synthesizing ammonia from hydrogen and atmospheric nitrogen. He was awarded the Nobel Prize in Chemistry in 1918. He presented the original experimental results in his Nobel lecture in 1920. This pap ...
Continuum thermodynamics of chemically reacting fluid mixtures
Continuum thermodynamics of chemically reacting fluid mixtures

An engine operates with 1 mol
An engine operates with 1 mol

... The work done by the system is the area enclosed by the cycle, where we assume that we start with the isothermal expansion. It is only in this expansion that heat is extracted from a reservoir. There is no heat transfer in the adiabatic expansion or compression. Thus we would completely convert heat ...
lecture 5 phase equilibria
lecture 5 phase equilibria

ParticleSystems - Computer Science and Engineering
ParticleSystems - Computer Science and Engineering

Thermodynamics and Phase Diagrams
Thermodynamics and Phase Diagrams

... Sometimes metastable states can be very short-lived, or at other times they can exist almost indefinitely. These are explained by the free-energy hump between the metastable and equilibrium states in Fig. 3.1. In general, higher free-energy humps, or energy barriers, lead to slower transformation ra ...
18.3 Standard Entropies and the Third Law of
18.3 Standard Entropies and the Third Law of

Pressure Data - Moore Chemistry
Pressure Data - Moore Chemistry

... The Temperature – Volume Relationship : Charles’ Law  Jacques Charles (1746-1823) was the scientist who developed the scientific law that relates temperature of a gas to its volume.  As the temperature of a gas increases, its volume increases and as the temperature of a gas decreases, its volume d ...
Lecture 17
Lecture 17

Document
Document

Chapter 10 The Mole
Chapter 10 The Mole

Supporting Text S1.
Supporting Text S1.

Document
Document

Mole-Mass Conversions
Mole-Mass Conversions

The Diffusion Equation A Multi
The Diffusion Equation A Multi

biphasic dosage forms suspensions and
biphasic dosage forms suspensions and

Notes Sheet - mychemcourse
Notes Sheet - mychemcourse

... Substances react according to definite ratios of numbers of particles (atoms, ions, formula units, or molecules). The following balanced chemical equation shows that two atoms of aluminum react with three molecules of iodine to form two formula units of aluminum iodide. 2Al(s) + 3I2(s)  2AlI3(s) If ...
Ch 8 LAN 7th Intro Chem Gases Liquids and Solids
Ch 8 LAN 7th Intro Chem Gases Liquids and Solids

Kinematics of Particles
Kinematics of Particles

chapter8_PC
chapter8_PC

Introduction Statistical Thermodynamics
Introduction Statistical Thermodynamics

... ⎛ ∂ ln Ω ⎞ ⎛ ∂ ln Ω ⎞ ln Ω E − Ei , N − N j , = ln Ω ( E, N ) − ⎜ ...
Application of the Langevin equation to fluid suspensions
Application of the Langevin equation to fluid suspensions

< 1 2 3 4 5 6 7 8 9 ... 25 >

Gibbs paradox

In statistical mechanics, a semi-classical derivation of the entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the ""mixing paradox"". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report