Boltzmann's constant

(noun)

The physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by Avogadro's number, NA.

Related Terms

Examples of Boltzmann's constant in the following topics:

  • Overview of Temperature and Kinetic Theory

    • The kinetic theory of gases describes a gas as a large number of small particles (atoms and molecules) in constant, random motion.
    • The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion.
    • The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classical ideal gas is called the Maxwell-Boltzmann distribution.
    • (k: Boltzmann's constant).
    • (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.

  • Equations of State

    • while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure
    • where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).
    • The proportionality factor is the universal gas constant, R, i.e.
    • where k is Boltzmann's constant and N is the number of molecules.

  • Isotherms

    • An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0.
    • An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0.
    • According to the ideal gas law, the value of the constant is NkT, where N is the number of molecules of gas and k is Boltzmann's constant.
    • This means that $p = {N k T \over V} = {\text{Constant} \over V}$ holds.
    • (This equation is derived in our Atom on "Constant Pressure" under kinetic theory.

  • Variation of Pressure With Depth

    • For any given liquid with constant density throughout, pressure increases with increasing depth.
    • For many liquids, the density can be assumed to be nearly constant throughout the volume of the liquid and, for virtually all practical applications, so can the acceleration due to gravity (g = 9.81 m/s2).
    • Thus the force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas).
    • The force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in this figure must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas)

  • Planck's Quantum Hypothesis and Black Body Radiation

    • A black body in thermal equilibrium (i.e. at a constant temperature) emits electromagnetic radiation called black body radiation.
    • where $B$ is the spectral radiance of the surface of the black body, $T$ is its absolute temperature, $\lambda$ is wavelength of the radiation, $k_B$ is the Boltzmann constant, $h$ is the Planck constant, and $c$ is the speed of light.
    • It is not a surprise that he introduced Planck constant $h = 6.626 \times 10^{-34} J \cdot s$ for the first time in his derivation of the Planck's law.

  • Internal Energy of an Ideal Gas

    • where k is the Boltzmann's constant.

  • Avogador's Number

    • The actual number of atoms or molecules in one mole is called Avogadro's constant (NA), in recognition of Italian scientist Amedeo Avogadro .
    • The value of Avogadro's constant, NA , has been found to equal 6.02×1023 mol−1.
    • Avogadro's constant is a scaling factor between macroscopic and microscopic (atomic scale) observations of nature.
    • As such, it provides the relation between other physical constants and properties.
    • For example, it establishes a relationship between the gas constant R and the Boltzmann constant k,

  • The Electron-Volt

    • Dividing electron volts by a constant with units of velocity results in a momentum.
    • where h is the Planck constant and c is the speed of light.
    • To convert to Kelvins, simply divide the value of 1 eV (in Joules) by the Boltzmann constant (1.3806505(24)×10-23 J/K).

  • Problem Solving

    • where R is the universal gas constant, and with it we can find values of the pressure P, volume V, temperature T, or number of moles n under a certain ideal thermodynamic condition.
    • where N is the number of particles in the gas and k is the Boltzmann constant.

  • Speed Distribution of Molecules

    • A gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.
    • Maxwell-Boltzmann distribution is a probability distribution.
    • The Maxwell-Boltzmann distribution of molecular speeds in an ideal gas.
    • The Maxwell-Boltzmann distribution is shifted to higher speeds and is broadened at higher temperatures.
    • Describe the shape and temperature dependence of the Maxwell-Boltzmann distribution curve