• # question_answer The dimensional formula for thermal resistance is : A) ${{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-2}}}{{\text{T}}^{\text{3}}}\text{ }\!\!\theta\!\!\text{ }$                     B) ${{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-2}}}{{\text{T}}^{\text{3}}}\text{ }\!\!\theta\!\!\text{ }$ C) $\text{M}{{\text{L}}^{\text{-2}}}{{\text{T}}^{2}}\text{ }\!\!\theta\!\!\text{ }$                 D) $\text{M}{{\text{L}}^{\text{-2}}}{{\text{T}}^{-2}}{{\text{ }\!\!\theta\!\!\text{ }}^{-1}}$

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 $\frac{({{\theta }_{1}}-{{\theta }_{2}})t}{Q}$ $=\frac{\theta T}{M\times ({{L}^{2}}{{T}^{-2}}{{\theta }^{-1}})}={{M}^{-1}}{{L}^{-2}}{{T}^{3}}\theta$