Temperature coefficient - Wikipedia Temperature coefficient A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R that changes by dR when the temperature changes by dT, the temperature coefficient α is defined by d R R = α d T. ( displaystyle ( \frac ( dR ) ( R ) ) = alpha , dT. ) Here α has the dimension of an inverse temperature and can be expressed e.g. in 1 / K or K. If the temperature coefficient itself does not vary too much with temperature, a linear approximation can be used to determine the value R of a property at a temperature T, given its value R at a reference temperature T : R ( T ) = R ( T 0 ) ( 1 + α Δ T ), ( displaystyle R ( T ) = R ( T_ ( 0 ) ) ( 1 + alpha Delta T ), ) where ΔT is the difference between T and T. For strongly temperature - dependent α, this approximation is only useful for small temperature differences ΔT. Temperature coefficients are specified for various applications, including electric and magnetic properties of materials as well as reactivity. The temperature coefficient of most of the reactions lies between - 2 & 3 Contents 1 Negative temperature coefficient 2 Reversible temperature coefficient 3 Electrical resistance 3.1 Positive temperature coefficient of resistance 3.2 Negative temperature coefficient of resistance 3.3 Negative temperature coefficient of resistance of a semiconductor 4 Temperature coefficient of elasticity 5 Temperature coefficient of reactivity 6 Mathematical derivation of temperature coefficient approximation 7 Units 8 References 9 External links 10 Bibliography Negative temperature coefficient This section may be confusing or unclear to readers. In particular, it 's unclear whether this refers to a general negative temperature coefficient or concerning electrical conductivity specifically. Please help us clarify the section. There might be a discussion about this on the talk page. ( January 2016 ) Most ceramics exhibit negative temperature dependence of resistance behaviour. This effect is governed by an Arrhenius equation over a wide range of temperatures : R = A ⋅ e B T ( displaystyle R = A cdot e ^ ( \frac ( B ) ( T ) ) ) where R is resistance, A and B are constants, and T is absolute temperature ( K ). The constant B is related to the energies required to form and move the charge carriers responsible for electrical conduction -- hence, as the value of B increases, the material becomes insulating. Practical and commercial NTC resistors aim to combine modest resistance with a value of B that provides good sensitivity to temperature. Such is the importance of the B constant value, that it is possible to characterize NTC thermistors using the B parameter equation : R = r ∞ e B T = R 0 e − B T 0 e B T ( displaystyle R = r ^ ( infty ) e ^ ( \frac ( B ) ( T ) ) = R_ ( 0 ) e ^ ( - ( \frac ( B ) ( T_ ( 0 ) ) ) ) e ^ ( \frac ( B ) ( T ) ) ) where R 0 ( displaystyle R_ ( 0 ) ) is resistance at temperature T 0 ( displaystyle T_ ( 0 ) ). Therefore, many materials that produce acceptable values of R 0 ( displaystyle R_ ( 0 ) ) include materials that have been alloyed or possess variable negative temperature coefficient ( NTC ), which occurs when a physical property ( such as thermal conductivity or electrical resistivity ) of a material lowers with increasing temperature, typically in a defined temperature range. For most materials, electrical resistivity will decrease with increasing temperature. Materials with a negative temperature coefficient have been used in floor heating since 1971. The negative temperature coefficient avoids excessive local heating beneath carpets, bean bag chairs, mattresses, etc., which can damage wooden floors, and may infrequently cause fires. Reversible temperature coefficient Residual magnetic flux density or Br changes with temperature and it is one of the important characteristics of magnet performance. Some applications, such as inertial gyroscopes and traveling - wave tubes ( TWTs ), need to have constant field over a wide temperature range. The reversible temperature coefficient ( RTC ) of Br is defined as : R T C = Δ B r B r Δ T × 100 ( displaystyle RTC = ( \frac ( Delta Br ) ( Br Delta T ) ) \times 100 ) To address these requirements, temperature compensated magnets were developed in the late 1970s. For conventional SmCo magnets, Br decreases as temperature increases. Conversely, for GdCo magnets, Br increases as temperature increases within certain temperature ranges. By combining samarium and gadolinium in the alloy, the temperature coefficient can be reduced to nearly zero. Electrical resistance See also : Table of materials ' resistivities The temperature dependence of electrical resistance and thus of electronic devices ( wires, resistors ) has to be taken into account when constructing devices and circuits. The temperature dependence of conductors is to a great degree linear and can be described by the approximation below. ρ ⁡ ( T ) = ρ 0 ( 1 + α 0 ( T − T 0 ) ) ( displaystyle operatorname ( \rho ) ( T ) = \rho _ ( 0 ) ( 1 + alpha _ ( 0 ) ( T - T_ ( 0 ) ) ) ) where α 0 = 1 ρ 0 ( δ ρ δ T ) T = T 0 ( displaystyle alpha _ ( 0 ) = ( \frac ( 1 ) ( \rho _ ( 0 ) ) ) left ( ( \frac ( delta \rho ) ( delta T ) ) \right ) _ ( T = T_ ( 0 ) ) ) ρ 0 ( displaystyle \rho _ ( 0 ) ) just corresponds to the specific resistance temperature coefficient at a specified reference value ( normally T = 0 ° C ) That of a semiconductor is however exponential : ρ ⁡ ( T ) = S α B T ( displaystyle operatorname ( \rho ) ( T ) = S alpha ^ ( \frac ( B ) ( T ) ) ) where S ( displaystyle S ) is defined as the cross sectional area and α ( displaystyle alpha ) and b ( displaystyle b ) are coefficients determining the shape of the function and the value of resistivity at a given temperature. For both, α ( displaystyle alpha ) is referred to as the resistance temperature coefficient. This property is used in devices such as thermistors. Positive temperature coefficient of resistance A positive temperature coefficient ( PTC ) refers to materials that experience an increase in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid increase with temperature, i.e. a higher coefficient. The higher the coefficient, the greater an increase in electrical resistance for a given temperature increase. A PTC material can be designed to reach a maximum temperature for a given input voltage, since at some point any further increase in temperature would be met with greater electrical resistance. Unlike linear resistance heating or NTC materials, PTC materials are inherently self - limiting. Some materials even have exponentially increasing temperature coefficient. Example of such a material is PTC rubber. Negative temperature coefficient of resistance A negative temperature coefficient ( NTC ) refers to materials that experience a decrease in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid decrease with temperature, i.e. a lower coefficient. The lower the coefficient, the greater a decrease in electrical resistance for a given temperature increase. NTC materials are used to create inrush current limiters ( because they present higher initial resistance until the current limiter reaches quiescent temperature ), temperature sensors and thermistors. Negative temperature coefficient of resistance of a semiconductor An increase in the temperature of a semiconducting material results in an increase in charge - carrier concentration. This results in a higher number of charge carriers available for recombination, increasing the conductivity of the semiconductor. The increasing conductivity causes the resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance. Temperature coefficient of elasticity The elastic modulus of elastic materials varies with temperature, typically decreasing with higher temperature. Temperature coefficient of reactivity In nuclear engineering, the temperature coefficient of reactivity is a measure of the change in reactivity ( resulting in a change in power ), brought about by a change in temperature of the reactor components or the reactor coolant. This may be defined as α T = ∂ ρ ∂ T ( displaystyle alpha _ ( T ) = ( \frac ( partial \rho ) ( partial T ) ) ) Where ρ ( displaystyle \rho ) is reactivity and T is temperature. The relationship shows that α T ( displaystyle alpha _ ( T ) ) is the value of the partial differential of reactivity with respect to temperature and is referred to as the `` temperature coefficient of reactivity ''. As a result, the temperature feedback provided by α T ( displaystyle alpha _ ( T ) ) has an intuitive application to passive nuclear safety. A negative α T ( displaystyle alpha _ ( T ) ) is broadly cited as important for reactor safety, but wide temperature variations across real reactors ( as opposed to a theoretical homogeneous reactor ) limit the usability of a single metric as a marker of reactor safety. In water moderated nuclear reactors, the bulk of reactivity changes with respect to temperature are brought about by changes in the temperature of the water. However each element of the core has a specific temperature coefficient of reactivity ( e.g. the fuel or cladding ). The mechanisms which drive fuel temperature coefficients of reactivity are different than water temperature coefficients. While water expands as temperature increases, causing longer neutron travel times during moderation, fuel material will not expand appreciably. Changes in reactivity in fuel due to temperature stem from a phenomenon known as doppler broadening, where resonance absorption of fast neutrons in fuel filler material prevents those neutrons from thermalizing ( slowing down ). Further information : Fuel temperature coefficient of reactivity Mathematical derivation of temperature coefficient approximation In its more general form, the temperature coefficient differential law is : d R d T = α R ( displaystyle ( \frac ( dR ) ( dT ) ) = alpha , R ) Where is defined : R 0 = R ( T 0 ) ( displaystyle R_ ( 0 ) = R ( T_ ( 0 ) ) ) And α ( displaystyle alpha ) is independent of T ( displaystyle T ). Integrating the temperature coefficient differential law : ∫ R 0 R ( T ) d R R = ∫ T 0 T α d T ⇒ ln ⁡ ( R ) R 0 R ( T ) = α ( T − T 0 ) ⇒ ln ⁡ ( R ( T ) R 0 ) = α ( T − T 0 ) ⇒ R ( T ) = R 0 e α ( T − T 0 ) ( displaystyle int _ ( R_ ( 0 ) ) ^ ( R ( T ) ) ( \frac ( dR ) ( R ) ) = int _ ( T_ ( 0 ) ) ^ ( T ) alpha , dT , , , Rightarrow ln ( R ) \vert _ ( R_ ( 0 ) ) ^ ( R ( T ) ) = alpha ( T - T_ ( 0 ) ) , , , Rightarrow ln left ( ( \frac ( R ( T ) ) ( R_ ( 0 ) ) ) \right ) = alpha ( T - T_ ( 0 ) ) , , , Rightarrow R ( T ) = R_ ( 0 ) e ^ ( alpha ( T - T_ ( 0 ) ) ) ) Applying the Taylor series approximation at the first order, in the proximity of T 0 ( displaystyle T_ ( 0 ) ), leads to : R ( T ) = R 0 ( 1 + α ( T − T 0 ) ) ( displaystyle R ( T ) = R_ ( 0 ) ( 1 + alpha ( T - T_ ( 0 ) ) ) ) Units The thermal coefficient of electrical circuit parts is sometimes specified as ppm / ° C. This specifies the fraction ( expressed in parts per million ) that its electrical characteristics will deviate when taken to a temperature above or below the operating temperature. References Jump up ^ `` About Us ''. Electron Energy Corporation. Jump up ^ Kasap, S.O. ( 2006 ). Principles of Electronic Materials and Devices ( Third ed. ). Mc - Graw Hill. p. 126. Jump up ^ Alenitsyn, Alexander G. ; Butikov, Eugene I. ; Kondraryez, Alexander S. ( 1997 ). Concise Handbook of Mathematics and Physics. CRC Press. pp. 331 -- 332. ISBN 0 - 8493 - 7745 - 5. Jump up ^ Duderstadt & Hamilton 1976, pp. 259 -- 261 Jump up ^ Duderstadt & Hamilton 1976, pp. 556 -- 559 External links Temperature Coefficient of a Thermistor - Ametherm Bibliography Duderstadt, Jame J. ; Hamilton, Louis J. ( 1976 ). Nuclear Reactor Analysis. Wiley. ISBN 0 - 471 - 22363 - 8. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Temperature_coefficient&oldid=792159213 '' Categories : Electric and magnetic fields in matter Electrical engineering Nuclear physics Hidden categories : Wikipedia articles needing clarification from January 2016 All Wikipedia articles needing clarification Talk Contents About Wikipedia Беларуская Čeština Deutsch Eesti Español فارسی Français Nederlands Norsk nynorsk Polski Português Русский Svenska Українська 中文 Edit links This page was last edited on 24 July 2017, at 20 : 51. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: the temperature coefficient of most of the reaction lies between
Answer: 2 & 3