To the Editor: The excellent article by R. W. Hakala in the February 1964 issue brings to mind another method proposed by A. Tobolsky some years ago.' While somewhat less general, this method relieves the student of the need to know anything about Jacobians and Bridgman's tables, yet keeps him from getting lost in the labyrinthine forest of thermodynamic derivatives. I n essence, the method is this: Having written down the usual differential expressions for dH, dA, dF, dE, C,, C,, and the four Maxwell relations, Tobolsky writes the complete differential containing the partial derivative sought. By appropriate substitution the expression is then converted into one where the differential coefficients are those of the desired independent variables. By equating terms with like coefficients one obtains two equations which can then be solved simnltaneously for the desired partial derivative. For example (this is the same one used in the February issue), to find (bE/bV), in terms of P and T , one writes dE
=
XdV
+
-T(aV/bT)pdP C,dT - P ( a v / a P ) ~ d PP(bV/bT)pdT = x ( a V / b P ) ~ d P X ( b V / b T ) p $2' YT(bV/bT)pdP Y C d T YVdP
+ +
+
By equating terms having the same differential coefficients one obtains
and by solving simultaneously for X,
+ YdH
where X is the quantity sought. Knowing that dH = TdS VdP, dE = TdS - PdV, and dS = (bS/bP), dP (bS/bT)&T, substitution gives
+ +
From the Maxwell relations and the fact that C, = T(b#/bT), the above expressions can be rewritten as
1
TOBOLSKY, A., J . Chem. Phys., 10,644 (1942).
Volume 41, Number 5, May 1964
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