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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 when the temperature changes by dT , the temperature coefficient α is defined by the following equation:
The Q 10 temperature coefficient is a measure of temperature sensitivity based on the chemical reactions. The Q 10 is calculated as: = / where; R is the rate T is the temperature in Celsius degrees or kelvin. Rewriting this equation, the assumption behind Q 10 is that the reaction rate R depends exponentially on temperature:
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
The coefficient α in the equation ... The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a ...
Some important aspects of this equation should be noted: (Alberty 2001), (Balian 2003), (Callen 1985) The thermodynamic space has k+2 dimensions; The differential quantities (U, S, V, N i) are all extensive quantities. The coefficients of the differential quantities are intensive quantities (temperature, pressure, chemical potential).
When stated in terms of temperature differences, Newton's law (with several further simplifying assumptions, such as a low Biot number and a temperature-independent heat capacity) results in a simple differential equation expressing temperature-difference as a function of time. The solution to that equation describes an exponential decrease of ...
In thermal engineering, the logarithmic mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger.
This equation uses the overall heat transfer coefficient of an unfouled heat exchanger and the fouling resistance to calculate the overall heat transfer coefficient of a fouled heat exchanger. The equation takes into account that the perimeter of the heat exchanger is different on the hot and cold sides.