The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as
where is the Boltzmann constant, is the speed of light, is the wavenumber, and (Greek letter nu) is the characteristic frequency of the oscillator.
The vibrational temperature is used commonly when finding the vibrational partition function.
| Molecule | ||
|---|---|---|
| N2 | 2446 cm−1 | 3521 K |
| O2 | 1568 cm−1 | 2256 K |
| F2 | 917 cm−1 | 1320 K |
| HF | 4138 cm−1 | 5957 K |
| HCl | 2991 cm−1 | 4303 K |
A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most scanning tunneling microscopes are built for use in ultra-high vacuum at temperatures approaching absolute zero, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C.
In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.
In fluid mechanics, the Grashof number is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number.
In the physical sciences, the wavenumber, also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time or radians per unit time.
In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".
In physics, the Rayleigh–Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments. For wavelength λ, it is where is the spectral radiance, is the speed of light, is the Boltzmann constant, and is the temperature in kelvins. For frequency , the expression is instead
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific heat in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box in contrast to the Einstein photoelectron model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence of the heat capacity of solids, which is proportional to – the Debye T 3 law. Similarly to the Einstein photoelectron model, it recovers the Dulong–Petit law at high temperatures. Due to simplifying assumptions, its accuracy suffers at intermediate temperatures.
Tunable diode laser absorption spectroscopy is a technique for measuring the concentration of certain species such as methane, water vapor and many more, in a gaseous mixture using tunable diode lasers and laser absorption spectrometry. The advantage of TDLAS over other techniques for concentration measurement is its ability to achieve very low detection limits. Apart from concentration, it is also possible to determine the temperature, pressure, velocity and mass flux of the gas under observation. TDLAS is by far the most common laser based absorption technique for quantitative assessments of species in gas phase.
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
Rotational–vibrational spectroscopy is a branch of molecular spectroscopy that is concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational transitions. When such transitions emit or absorb photons, the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy. Since changes in rotational energy levels are typically much smaller than changes in vibrational energy levels, changes in rotational state are said to give fine structure to the vibrational spectrum. For a given vibrational transition, the same theoretical treatment as for pure rotational spectroscopy gives the rotational quantum numbers, energy levels, and selection rules. In linear and spherical top molecules, rotational lines are found as simple progressions at both higher and lower frequencies relative to the pure vibration frequency. In symmetric top molecules the transitions are classified as parallel when the dipole moment change is parallel to the principal axis of rotation, and perpendicular when the change is perpendicular to that axis. The ro-vibrational spectrum of the asymmetric rotor water is important because of the presence of water vapor in the atmosphere.
Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The rotational spectrum of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy where rotational, vibrational and electronic energy changes occur simultaneously.
In chemistry and physics, Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes-Raman scattering.
In thermodynamics, the specific volume of a substance is the quotient of the substance's volume to its mass :
The vibrational partition function traditionally refers to the component of the canonical partition function resulting from the vibrational degrees of freedom of a system. The vibrational partition function is only well-defined in model systems where the vibrational motion is relatively uncoupled with the system's other degrees of freedom.
The characteristic rotational temperature is commonly used in statistical thermodynamics to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties. It has units of temperature and is defined as
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 μm.
In chemistry, the rotational partition function relates the rotational degrees of freedom to the rotational part of the energy.
Vibronic spectroscopy is a branch of molecular spectroscopy concerned with vibronic transitions: the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. In the gas phase, vibronic transitions are also accompanied by changes in rotational energy.
The Planck relation is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: The constant of proportionality, h, is known as the Planck constant. Several equivalent forms of the relation exist, including in terms of angular frequency ω: where . Written using the symbol f for frequency, the relation is
In chemistry, NMR line broadening techniques can be used to determine the rate constant and the Gibbs free energy of exchange reactions of two different chemical compounds. If the two species are in equilibrium and exchange to each other, peaks of both species get broadened in the spectrum. This observation of broadened peaks can be used to obtain kinetic and thermodynamic information of the exchange reaction.
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