Thermo Square

S H P
[pic]
V A TThe Thermodynamic Square

The Thermodynamic Square (see above) is a mnemonic diagram that can be used to obtain a number of the more useful thermodynamic relations (Max Born and F. O. Koenig).There are several different types of these diagrams (see, e.g., H. B. Callen, Thermodynamics, John Wiley & Sons, New York, 1960) applicable to thermodynamic systems of various types. The one presentedhere is the "best known and most generally useful of these diagrams. It is applicable to thermodynamic systems of fixed mass and composition involving only expansion work.
In the diagram each ofthe thermodynamic energy functions U, H, G, and A is placed
on a side of the square and is flanked by its natural independent variables: U = U(S, V); H = H(S, P); G = G(P, T) and A = A(V, T). Towrite the differential expression for any of these functions in terms of differentials of its natural independent variables we need only note that the coefficient of the differential of theindependent variable is placed diagonally opposite this variable on the square. An arrow pointing away from a natural variable indicates a positive sign. Thus, e.g., we obtain for dGdG = -SdT + VdP,

and for dU

dU = TdS - PdV,

and so forth. The Maxwell relations can also be read off the diagram usingthe corners of the square with the signs being determined by the placement of the arrows. If the arrows are symmetrically placed then the sign is plus. For example, from the orientationS P
V T V T

we obtain (∂s/∂v)T = (∂p/∂T)V.. Whereas from the orientation...