**Unformatted text preview: **T Q S T T Q S T â€² âˆ‚ âˆ‚ = âˆ† â€² âˆ‚ âˆ‚ âˆ‚ âˆ‚ = âˆ† âˆ‚ âˆ‚ Î» , Î» and so conclude that T T â€² = immediately; this is equivalent to treating the differentiation as a related rate problem, as 2 2 1 1 = â€² â€² + = âˆ† â€² dT T d T c m T c m S T d d and using T T c m c m dT T d â€² =-= â€² gives 2 2 1 1 with a great savings of algebra. c) The final state of the system will be that for which no further entropy change is possible. If , T T â€² < it is possible for the temperatures to approach each other while increasing the total entropy, but when , T T â€² = no further spontaneous heat exchange is possible....

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