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In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities (often approximated by concentrations) of the chemical species undergoing ...
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
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
Also, the Borel measure and the Lebesgue measure coincide on the Borel sets (i.e., () = for every Borel measurable set, where is the Borel measure described above). This idea extends to finite-dimensional spaces R n {\displaystyle \mathbb {R} ^{n}} (the Cramér–Wold theorem , below) but does not hold, in general, for infinite-dimensional spaces.
The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates, their absolute difference.Thus if and are two points on the real line, then the distance between them is given by: [1]
where C is the heat capacity, it follows that: = The heat capacity depends on how the external variables of the system are changed when the heat is supplied. If the only external variable of the system is the volume, then we can write:
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In mathematics, the Fréchet derivative is a derivative defined on normed spaces.Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative used widely in the calculus of variations.