A) \[{{t}_{2}}:{{t}_{1}}\]
B) \[{{t}_{1}}:{{t}_{2}}\]
C) \[t_{1}^{2}:t_{2}^{2}\]
D) \[t_{2}^{2}:t_{1}^{2}\]
Correct Answer: A
Solution :
We know that Relation between temperature gradient (TG) and thermal conductivity (K) So, \[\frac{d\theta }{dt}=-KA\frac{d\theta }{dx}=-KA\times (TG)\] i.e., \[TG\propto \frac{1}{K}\left( \frac{d\theta }{dt}=\text{constant} \right)\] or \[K\propto \frac{1}{T}\] \[{{K}_{1}}\propto \frac{1}{{{t}_{1}}}\] ?(i) \[{{K}_{2}}\propto \frac{1}{{{t}_{2}}}\] ?(ii) From the Eqs. (i) and (ii), we get \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{1/{{t}_{1}}}{1/{{t}_{2}}}\] \[{{K}_{1}}:{{K}_{2}}={{t}_{2}}:{{t}_{1}}\]
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