A comparison is made of two versions of the acoustic-mismatch theory of the thermal boundary resistance R which occurs at the interface between a pair of solids. The most recent version predicts R→0 as the two solids become identical, while the earlier version indicates a finite R as the interface essentially vanishes. It is shown that the two versions make different assumptions as to what a thermometer measures and that, if appropriate thermometers are used, both versions give the same result. This conclusion is supported by experimental evidence.
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Katerberg et al. (1977) studied this question.