temperature coefficient of resistivity

(noun)

An empirical quantity, denoted by α, which describes the change in resistance or resistivity of a material with temperature.

Related Terms

Examples of temperature coefficient of resistivity in the following topics:

  • Dependence of Resistance on Temperature

    • The resistivity of all materials depends on temperature.
    • where ρ0 is the original resistivity and α is the temperature coefficient of resistivity.
    • The temperature coefficient is typically +3×10−3 K−1 to +6×10−3 K−1 for metals near room temperature.
    • (Examination of the coefficients of linear expansion shows them to be about two orders of magnitude less than typical temperature coefficients of resistivity, and so the effect of temperature on L and A is about two orders of magnitude less than on ρ. ) Thus,
    • is the temperature dependence of the resistance of an object, where R0 is the original resistance and R is the resistance after a temperature change T.

  • Volume Expansion

    • The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient. illustrates that, in general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions.
    • Mathematical definitions of these coefficients are defined below for solids, liquids, and gasses:
    • In the case of a gas, the fact that the pressure is held constant is important, as the volume of a gas will vary appreciably with pressure as well as with temperature.
    • where V is the volume of the material, and is dV/dT the rate of change of that volume with temperature.
    • (and from the definitions of the thermal coefficients), we arrive at:

  • Area Expansion

    • The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature.
    • It is the fractional change in area per degree of temperature change.
    • This equation works well as long as the linear expansion coefficient does not change much over the change in temperature $\Delta T$.
    • For isotropic materials, and for small expansions, the linear thermal expansion coefficient is one half of the area coefficient.
    • Express the area thermal expansion coefficient in the form of an equation

  • Linear Expansion

    • The degree of expansion divided by the change in temperature is called the material's coefficient of thermal expansion; it generally varies with temperature.
    • To a first approximation, the change in length measurements of an object (linear dimension as opposed to, for example, volumetric dimension) due to thermal expansion is related to temperature change by a linear expansion coefficient.
    • It is the fractional change in length per degree of temperature change.
    • From the definition of the expansion coefficient, the change in the linear dimension $\Delta L$ over a temperature range $\Delta T$ can be estimated to be:
    • This equation works well as long as the linear-expansion coefficient does not change much over the change in temperature.

  • Temperature

    • Although there is an entire field of study devoted to measuring temperature (thermometry), the focus of this section is on the fundamental measurements of temperature.
    • Fahrenheit was working with tubes filled with mercury, which has a very high coefficient of thermal expansion.
    • The bimetallic strips are made from two dissimilar metals bonded together, with each metal having a different coefficient of thermal expansion.
    • Temperature itself is the measurement of the average kinetic energy of a substance.
    • A comparison of temperature scales table illustrates a variety of temperature scales, some of which are no longer used.

  • Water’s High Heat Capacity

    • Water is able to absorb a high amount of heat before increasing in temperature, allowing humans to maintain body temperature.
    • When the temperature of water decreases, the hydrogen bonds are formed and release a considerable amount of energy.
    • Specific heat is defined as the amount of heat one gram of a substance must absorb or lose to change its temperature by one degree Celsius.
    • The resistance to sudden temperature changes makes water an excellent habitat, allowing organisms to survive without experiencing wide temperature fluctuation.
    • For example, the temperature of your body does not drastically drop to the same temperature as the outside temperature while you are skiing or playing in the snow.

  • Thermal Stresses

    • Thermal expansion is the change in size or volume of a given mass with temperature.
    • An increase in temperature implies an increase in the kinetic energy of the individual atoms.
    • where ΔL is the change in length L, ΔT is the change in temperature, and α is the coefficient of linear expansion, which varies slightly with temperature.
    • One challenge is to find a coating that has an expansion coefficient similar to that of metal.
    • Metal fillings (gold, silver, etc.) are being replaced by composite fillings (porcelain), which have smaller coefficients of expansion, and are closer to those of teeth.

  • Temperature and Superconductivity

    • Superconductivity is a phenomenon of zero electrical resistance and expulsion of magnetic fields in certain materials below a critical temp.
    • Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature.
    • Solid mercury, for example, has a critical temperature of 4.2 K.
    • For example, YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K; mercury-based cuprates have been found with critical temperatures in excess of 130 K.
    • Behavior of heat capacity (cv, blue) and resistivity (ρ, green) at the superconducting phase transition.

  • Relative Resistance of Microbes

    • Different microbial structures and types of microbial cells have different level of resistance to antimicrobial agents.
    • Different microbial structures and types of microbial cells have different level of resistance to antimicrobial agents used to eliminate them.
    • Endospores are considered the most resistant structure of microbes .
    • As cysts, protozoa can survive harsh conditions, such as exposure to extreme temperatures or harmful chemicals, or long periods without access to nutrients, water, or oxygen for a period of time.
    • Staphylococcus aureus is one of the major resistant pathogens.

  • Regioselectivity and Lewis Acid Catalysis

    • Despite disubstitution of the diene and the dienophile in this case, the endo adduct is formed with high regioselectivity and yield at a relatively low temperature.
    • In the case of 1,3-butadiene, shown in the diagram below, the lowest energy pi-orbital (π1) has smaller orbital coefficients at C-1 and C-4, and larger coefficients at C-2 and C-3.
    • The remaining three pi-orbitals have similar coefficients (± 0.37 or 0.60), but the location of the higher coefficient shifts to the end carbons in the HOMO and LUMO orbitals (π2 & π3 respectively).
    • Unsymmetrical substitution of a diene or dienophile perturbs the orbital coefficients in an unsymmetrical fashion.
    • In many cases, this analysis of HOMO and LUMO orbital coefficients also provides a good explanation for the beneficial influence of Lewis acid catalysis.