By Hitchcock F.L.
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Extra info for [Article] A Classification of Quadratic Vector Functions
Such an analysis demonstrates that equilibrium requires that the heat capacity at constant volume and the isothermal compressibility must be positive. Indeed, if the heat capacity of a body was negative, it could never achieve thermal equilibrium with its initially higher temperature surroundings (according to the Clausius postulate, heat would ﬂow from the warmer surroundings to the body, but since cV < 0 dT ¼ Q/cV < 0, the temperature of the body would decrease). e. if the surroundings exerted a positive pressure on the body, the body would expand).
The former is easily measured, while the latter requires the additional knowledge of the molecular weight (and a trivial calculation). We are often called upon to convert between one deﬁnition of concentration to another. Here is an example of how we can convert from molality to molar fraction in a binary (two-component) solution. We start from a formal deﬁnition of that concentration that we wish to obtain: n2 n2 m2 x2 ¼ ¼ ¼ , n1 þ n2 w1 =(M1 =1000) þ n2 1000=M1 þ m2 where M1 is molar weight of the solvent expressed in g/mole.
62) corresponds to equilibrium, that is, the conditions of equilibrium are dA ¼ 0, at T ¼ const, V ¼ const (1:63) dG ¼ 0, at T ¼ const, p ¼ const: (1:64) When the system is in equilibrium, the process no longer spontaneously proceeds in any direction. This implies that if a thermodynamic system is in equilibrium it cannot spontaneously leave this state. Review questions 1. What are the dimensions of the Helmholtz and Gibbs free energies? 2. Under what conditions is the equation ÁG ¼ ÁH À TÁS valid?
[Article] A Classification of Quadratic Vector Functions by Hitchcock F.L.