• 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
Unit 1, Lecture 3 - Massey University
Unit 1, Lecture 3 - Massey University

Molar Heat Capacities of an Ideal Gas
Molar Heat Capacities of an Ideal Gas

Notes on the First Law of Thermodynamics Chemistry CHEM 213W
Notes on the First Law of Thermodynamics Chemistry CHEM 213W

... sorts of processes is known as pressure-volume work. Note that the work done is not a state function--it depends on the pressure exerted on the piston (the path) and is not simply a function of the state of the gas in the piston. To stress this fact, the notation d− will be used for infinitesimal ch ...
Chapter Summary
Chapter Summary

Measuring kinetic energy changes in the mesoscale with low
Measuring kinetic energy changes in the mesoscale with low

... Author to whom correspondence should be addressed. Electronic mail: [email protected] ...
PHYSICAL SCIENCE CHAPTER 3 STATES OF MATTER
PHYSICAL SCIENCE CHAPTER 3 STATES OF MATTER

Measuring kinetic energy changes in the mesoscale with low
Measuring kinetic energy changes in the mesoscale with low

CHAPTER TWO The First Law and Other Basic Concepts
CHAPTER TWO The First Law and Other Basic Concepts

NkT PV = nRT PV = Pa pressure P = m volume V = moles n particles
NkT PV = nRT PV = Pa pressure P = m volume V = moles n particles

... Diatomic gas with 2 degrees of vibration freedom and 2 degrees of rotational freedom in addition to the 3 translation degrees of freedom. ...
12 Chemical Potential
12 Chemical Potential

... particle energy  consists of the part that depends on concentration and temperature given by kT ln N / N 0   0 and any external potential energy U.   kT ln N N 0   0  U ...
Chapter 9: Thermodynamic Processes and Thermochemistry
Chapter 9: Thermodynamic Processes and Thermochemistry

BCJ0205-15 Thermal phenomena (3-1-4)
BCJ0205-15 Thermal phenomena (3-1-4)

Important Equations in Physics (A2) Unit 1: Non
Important Equations in Physics (A2) Unit 1: Non

... P=pressure, V=volume, T=temp in Kelvin, n number of moles, R=universal gas constant per mole=8.3Jmole-1K-1. 6 Ideal Gas - gas that obeys ideal gas equation at all pressures, volumes, temperatures, - molecules do not exert forces on each other when collide, - the collision between the molecules is pe ...
Lecture-VIII
Lecture-VIII

Corporate Profile
Corporate Profile

Thermodynamics - Issaquah Connect
Thermodynamics - Issaquah Connect

Chapter 6:
Chapter 6:

... a. Thermochemical equations for the individual steps of a reaction sequence may be multiplied to find the total energy of the overall reaction. b. Thermochemical equations for the individual steps of a reaction sequence may be combined by multiplication or addition to find the total energy of the o ...
Lect1.LawsofThr
Lect1.LawsofThr

0.1 Minimum Principles and Thermodynamic Potentials
0.1 Minimum Principles and Thermodynamic Potentials

Ionic Equations
Ionic Equations

FIRST LAW OF THERMODYNAMICS
FIRST LAW OF THERMODYNAMICS

... That is, heat interaction is equal to the change in internal energy of the gas. If the system contains a mass m equal of an ideal gas, then Q = ΔU = mCv (T2 –T1) The path followed by the gas is shown on a P-V diagram. Now consider the fluid contained in a rigid vessel as shown. The vessel is rigid a ...
Measuring kinetic energy changes in the mesoscale with low
Measuring kinetic energy changes in the mesoscale with low

Thermodynamics Temperature Scales Thermal Expansion and Stress
Thermodynamics Temperature Scales Thermal Expansion and Stress

IB Option B.2 Thermodynamics Feb 21 Agenda
IB Option B.2 Thermodynamics Feb 21 Agenda

1st Set of Notes - Idaho State University
1st Set of Notes - Idaho State University

... The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol." ...
< 1 ... 19 20 21 22 23 24 25 26 27 >

Equipartition theorem



In classical statistical mechanics, the equipartition theorem is a general formula that relates the temperature of a system with its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in the translational motion of a molecule should equal that of its rotational motions.The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal gas has an average kinetic energy of (3/2)kBT in thermal equilibrium, where kB is the Boltzmann constant and T is the (thermodynamic) temperature. More generally, it can be applied to any classical system in thermal equilibrium, no matter how complicated. The equipartition theorem can be used to derive the ideal gas law, and the Dulong–Petit law for the specific heat capacities of solids. It can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered.Although the equipartition theorem makes very accurate predictions in certain conditions, it becomes inaccurate when quantum effects are significant, such as at low temperatures. When the thermal energy kBT is smaller than the quantum energy spacing in a particular degree of freedom, the average energy and heat capacity of this degree of freedom are less than the values predicted by equipartition. Such a degree of freedom is said to be ""frozen out"" when the thermal energy is much smaller than this spacing. For example, the heat capacity of a solid decreases at low temperatures as various types of motion become frozen out, rather than remaining constant as predicted by equipartition. Such decreases in heat capacity were among the first signs to physicists of the 19th century that classical physics was incorrect and that a new, more subtle, scientific model was required. Along with other evidence, equipartition's failure to model black-body radiation—also known as the ultraviolet catastrophe—led Max Planck to suggest that energy in the oscillators in an object, which emit light, were quantized, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report