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Q. Dimensional formula for entropy is identical to that of

CMC MedicalCMC Medical 2011

Solution:

$ \text{Entropy}=\frac{\text{Heat}\,\text{absorbed}}{\text{Temperature}} $ $ \Rightarrow $ $ S=\frac{Q}{T} $ $ \Rightarrow $ $ [S]=[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}] $ Also, $ E=\frac{1}{2}{{k}_{B}}T $ where $ {{k}_{B}} $ is Boltzmann constant. $ \Rightarrow $ $ [{{k}_{B}}]=\frac{[E]}{[T]}=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[K]}=[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}] $ Hence, dimensional formula of entropy is same as that of Boltzmann constant.