Download Entropy for Biologists. An Introduction to Thermodynamics by Harold J. Morowitz PDF

By Harold J. Morowitz

Entropy for Biologists: An creation to Thermodynamics [Paperback] [Jan 01, 1970] Morowitz, Harold J. ... 0125071566

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D. THE M E A S U R A B I L I T Y OF E N T R O P Y The entropy of a pure substance can always be determined relative to some arbitrary standard state. If the standard state is defined by some values of the pressure and temperature PQ and Tq, any arbitrary state can be represented by some values of Ρ and T. Since entropy is an exten­ sive function, and depends on the amount of material in the system, the entropy of pure substances is generally determined as entropy per gram or entropy per mole. W e will adopt the convention of using entropy per mole.

A reversible path must be followed to P, T. First reversibly heat the system at con­ stant pressure from TQ to Τ and then place it in contact with a reservoir at temperature Τ and expand or contract the system until the pressure goes from PQ to P. The change in entropy is therefore S - So= r'dQ —+ Τ ho r'dQ — Jp^ Τ (6-37) Equation (6-37) can be rewritten in the following form: (dQldT)pdT τ ^ 1 r^dQ ^TJ Po\dV dV (6-38) τ The quantity (dQldT)p is the specific heat at constant pressure Cp while {dQldV)j is the heat of compression at constant temperature h^.

T o prove the logical equivalence of the two statements we will use formal symbolic logic, utilizing the following symbols: a. b. c. Equivalence =, Λ = B, Ah logically equivalent to B. Implication ZD ; A :=> B; A implies B, the truth of A implies the truth of B. Negation — ; —A, which is read "not A either A is true or -A \s true. W e now quote a result of formal logic which seems intuitively clear without formal proof. A = Β if A Β and Β z:> A, that is, A is equiva­ lent to Β if the truth of A implies the truth of Β and the truth of Β implies the truth of A.

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