Abstract
Typical three-dimensional problems are the (p, v,T) properties of a gas or the vapour pressure of a two-component mixture. Here we have three variables and an equation connecting them, so that two variables are independent (see Section 1.4). In such cases the geometrical method is to draw a three-dimensional diagram and then to consider two- dimensional sections, which apply when the third variable is held constant. Thus we may consider p against v at constant T for a gas, or p against mole fraction x at constant T for the mixture. The corresponding analytical problem is: Given a function z = z (x, y) how does z vary with x when y is kept constant, and with y when x is kept constant?
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© 1984 P. G. Francis
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Francis, P.G. (1984). Differential calculus in three or more dimensions; partial differentiation. In: Mathematics for Chemists. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5552-3_3
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DOI: https://doi.org/10.1007/978-94-009-5552-3_3
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-94-009-5552-3
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