A) \[\frac{A\alpha (T_{1}^{2}-T_{2}^{2})}{\ell }\]
B) \[\frac{A\alpha (T_{1}^{2}+T_{2}^{2})}{\ell }\]
C) \[\frac{A\alpha (T_{1}^{2}+T_{2}^{2})}{3\ell }\]
D) \[\frac{A\alpha (T_{1}^{2}-T_{2}^{2})}{2\ell }\]
Correct Answer: D
Solution :
| [d] Heat current \[i=-kAdT\] |
| \[id=-kA\,dT\] |
| \[i\int\limits_{0}^{\ell }{dx}\text{ }=-A\alpha \int\limits_{{{T}_{1}}}^{{{T}_{2}}}{T}\text{ }dT\] |
| \[\Rightarrow \] \[i\,\ell =-A\,\alpha \frac{\left( T_{2}^{2}-T_{1}^{2} \right)}{2}\] |
| \[\Rightarrow \] \[i=\frac{A \alpha \left( T_{1}^{2}-T_{2}^{2} \right)}{2\ell }\] |
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