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Modern Thermodynamics for Chemists and Biochemists$
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Dennis Sherwood and Paul Dalby

Print publication date: 2018

Print ISBN-13: 9780198782957

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198782957.001.0001

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Thermodynamics and mathematics

Thermodynamics and mathematics

(p.76) 4 Thermodynamics and mathematics
Modern Thermodynamics for Chemists and Biochemists

Dennis Sherwood

Paul Dalby

Oxford University Press

Most school mathematics is about how one variable, y, varies with respect to one other variable, x, according to an equation such as y = 3x2. Equations like this underpin the student’s knowledge of algebra, and differential and integral calculus. Thermodynamics, however, is necessarily about how a variable, such as the pressure P, varies with respect not to one but to three variables simultaneously – for example, the mole number n, the volume V, and the temperature T. This makes the algebra of thermodynamics more complex, and also implies that mutual changes between pairs of variables is described not in terms of total derivatives of the form dy/dx, but rather by partial derivatives of the form (∂P/∂T)V. Many students find the leap from dy/dx to (∂P/∂T)V very difficult - the purpose of this chapter is therefore to build the reader’s confidence in understanding, and manipulating, functions of two and three variables.

Keywords:   functions of two and three variables, partial derivatives, systems of constant mass, pure substances, mixtures

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