A) \[[ML{{T}^{-1}}{{\theta }^{-1}}]\]
B) \[[ML{{T}^{-3}}{{\theta }^{-1}}]\]
C) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{2}}\text{L}{{\text{T}}^{\text{-3}}}{{\text{ }\!\!\theta\!\!\text{ }}^{-2}}\text{ }\!\!]\!\!\text{ }\]
D) \[[M{{L}^{2}}{{T}^{-2}}\theta ]\]
Correct Answer: B
Solution :
Key Idea: Substituting dimensions for corresponding quantities in the relation having coefficient of thermal conductivity. Heat \[\Delta Q\] transferred through a rod of length L and area A in time At is \[\Delta Q=KA\left( \frac{{{T}_{1}}-{{T}_{2}}}{L} \right)\Delta t\] where K = Coefficient of thermal conductivity \[{{T}_{1}}-{{T}_{2}}=\]temperature difference \[\therefore \] \[K=\frac{\Delta Q\times L}{A({{T}_{1}}-{{T}_{2}})\Delta t}\] ?. (i) Substituting dimensions for corresponding quantity in Eq. (i), we have \[[K]=\frac{[M{{L}^{2}}{{T}^{-1}}][L]}{[{{L}^{2}}]\,[\theta ]\,[T]}\] \[=[ML{{T}^{-3}}{{\theta }^{-1}}]\]
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