thermal equilibrium

Examples of thermal equilibrium in the following topics:

• The Zeroth Law of Thermodynamics

  • The Zeroth Law of Thermodynamics states that systems in thermal equilibrium are at the same temperature.
  • Systems are in thermal equilibrium if they do not transfer heat, even though they are in a position to do so, based on other factors.
  • If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.
  • Temperature is the quantity that is always the same for all systems in thermal equilibrium with one another.
  • The double arrow represents thermal equilibrium between systems.

• A Review of the Zeroth Law

  • The Zeroth Law of Thermodynamics states: If two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C.
  • Two systems are in thermal equilibrium if they could transfer heat between each other, but don't.
  • Indeed, experiments have shown that if two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system C, then A is also in thermal equilibrium with C.
  • The objects are then in thermal equilibrium, and no further changes will occur.
  • Thus, if enough time is allowed for this transfer of heat to run its course, the temperature a thermometer registers does represent the system with which it achieves thermal equilibrium.

• LTE

  • To derive these relations we have not made any assumptions about whether the photons or the matter are in thermal equilibrium with themselves or each other.
  • An extremely useful assumption is that the matter is in thermal equilibrium at least locally (Local Thermodynamic Equilibrium).
  • In this case the ratio of the number of atoms in the various states is determined by the condition of thermodynamic equilibrium
  • Because the source function equals the blackbody function, does this mean that sources in local thermodynamic equilibrium emit blackbody radiation?

• Thermal Bremsstrahlung Absorption

  • If we assume that the photon field is in thermal equilibrium with the electrons and ion we can obtain an expression for the corresponding absorption,

• A Physical Aside: Intensity and Flux

  • Blackbody radiation is a radiation field that is in thermal equilibrium with itself.
  • In general we will find it convenient to think about radiation that is in equilibrium with some material or its enclosure.
  • Using detailed balance between two enclosures in equilibrium with each other and the enclosed radiation we can quickly derive several important properties of blackbody radiation.

• Thermal Distributions of Atoms

  • In thermal equilibrium the number of atoms in a particular state is proportional to $ge^{-\beta E}$ where $\beta=1/kT$ and $g$ is the statistical weight or degeneracy of the state (for $L-S-$ coupling $g=2(2J+1)$), so we find that

• Non-Thermal Emission

  • An extreme example of non-thermal emission is the maser.For atoms in thermodynamic equilibrium we have
  • which means that the absorption coefficient is always positive in thermodynamic equilibrium.

• Thermal Radiation

  • Let's imagine a blackbody enclosure, and we stick some material inside the enclosure and wait until it reaches equilibrium with the radiation field, $I_\nu = B_\nu(T)$.
  • $\displaystyle \text{Another Kirchoff's Law: }S_\nu = B_\nu(T) \text{ for a thermal emitter}$
  • Because $I_\nu=B_\nu(T)$ outside of the thermal emitting material and $S_\nu=B_\nu(T)$ within the material, we find that $I_\nu=B_\nu(T)$ through out the enclosure.
  • If we remove the thermal emitter from the blackbody enclosure we can see the difference between thermal radiation and blackbody radiation.
  • A thermal emitter has $S_\nu = B_\nu(T)$,$B_\nu(T)$ so the radiation field approaches $B_\nu(T)$ (blackbody radiation) only at large optical depth.

• Linear Expansion

  • Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.
  • Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.
  • (An example of this is the buckling of railroad track, as seen in . ) Atoms and molecules in a solid, for instance, constantly oscillate around its equilibrium point.
  • This kind of excitation is called thermal motion.
  • In the diagram, (b) shows that as the substance is heated, the equilibrium (or average) particle-particle distance increases.

• Thermal Instability

  • If the power absorbed and generated within the gas equals the power emitted by the gas, the temperature of the gas will remain constant and equilibrium is achieved.
  • The question remains whether this equilibrium is stable.
  • Heuristically we can see that if the cooling rate increases faster with temperature than the heating rate, then a slight increase in temperature will result in the gas cooling faster and the temperature returning to its equilibrium value.