A) \[{{M}^{-1}}{{L}^{-2}}{{T}^{3}}\theta \]
B) \[{{M}^{-1}}{{L}^{-2}}{{T}^{-3}}\theta \]
C) \[M{{L}^{2}}{{T}^{-2}}\theta \]
D) \[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-2}}\]
Correct Answer: A
Solution :
When thermal conductivity is K, thermal resistivity is \[\frac{1}{K}\], then thermal resistance \[R=\frac{1\times L}{KA}\] Now heat conducted is given by \[\frac{{{Q}_{1}}}{t}={{\theta }_{1}}\frac{kA({{\theta }_{1}}-{{\theta }_{2}})}{L}=\frac{{{\theta }_{1}}-{{\theta }_{2}}}{R}\] Therefore, dimensions of R = dimensions of \[\frac{({{\theta }_{1}}-{{\theta }_{2}})t}{Q}\] \[=\frac{\theta T}{M\times ({{L}^{2}}{{T}^{-2}}{{\theta }^{-1}})\theta }={{M}^{-1}}{{L}^{-2}}{{T}^{3}}\theta \]
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