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The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
Where it is desirable to know the actual dry solids content, empirical correction formulas can be developed based on calibrations with solutions similar to those being tested. For example, in sugar refining, dissolved solids can be accurately estimated from refractive index measurement corrected by an optical rotation (polarization) measurement.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons.
There are more detailed generalized compressibility factor graphs based on as many as 25 or more different pure gases, such as the Nelson-Obert graphs. Such graphs are said to have an accuracy within 1–2 percent for Z {\displaystyle Z} values greater than 0.6 and within 4–6 percent for Z {\displaystyle Z} values of 0.3–0.6.
where the final substitution, N 0 = e C, is obtained by evaluating the equation at t = 0, as N 0 is defined as being the quantity at t = 0. This is the form of the equation that is most commonly used to describe exponential decay. Any one of decay constant, mean lifetime, or half-life is sufficient to characterise the decay.
The gem is placed on a high refractive index prism and illuminated from below. A high refractive index contact liquid is used to achieve optical contact between the gem and the prism. At small incidence angles most of the light will be transmitted into the gem, but at high angles total internal reflection will occur in the prism.
In that case, the result of the original formula would be called the sample standard deviation and denoted by instead of . Dividing by rather than by gives an unbiased estimate of the variance of the larger parent population. This is known as Bessel's correction.