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Question

Physics Question on Dimensional Analysis

The dimensional formula for entropy is

A

[ MLT2K1MLT^{- 2}K^{- 1} ]

B

[ ML2T2ML^{2}T^{- 2} ]

C

[ ML2T2K1ML^{2}T^{- 2}K^{- 1} ]

D

[ ML2T2K1ML^{- 2}T^{- 2}K^{- 1} ]

Answer

[ ML2T2K1ML^{2}T^{- 2}K^{- 1} ]

Explanation

Solution

Entropy=heattemperatureEntropy=\frac{h e a t}{t e m p e r a t u r e} \, (?Q=T?S)\left(\right. \text{?} Q = T \text{?} S \left.\right) [Entropy]= QT=[ML2T2][K]=[ML2T2K1]\frac{Q}{T}=\frac{\left[\right. M L^{2} T^{- 2} \left]\right.}{\left[\right. K \left]\right.}=\left[\right.ML^{2}T^{- 2}K^{- 1}\left]\right.