A thermodynamic invariant in the form of the ratio of a vibrational frequen
cy in an anharmonic solid to the temperature in adiabatic processes is deri
ved. The adiabatic invariance established is used to derive in a simple man
ner an expression for the temperature change due to elastic adiabatic loadi
ng of solids (Kelvin's equation). (C) 1999 American Institute of Physics. [
S1063-7834(99)02801-4].