A) \[\frac{1}{(\sqrt{2}+1)}\]
B) \[\frac{3}{(\sqrt{2}+1)}\]
C) \[\frac{1}{2(\sqrt{2}-1)}\]
D) \[\frac{1}{\sqrt{3}(\sqrt{2}-1)}\]
Correct Answer: B
Solution :
\[\because \] \[{{T}_{B}}>{{T}_{A}}\] Þ Heat will flow B to A via two paths (i) B to A (ii) and along BCA as shown. Rate of flow of heat in path BCA will be same i.e. \[{{\left( \frac{Q}{t} \right)}_{BC}}={{\left( \frac{Q}{t} \right)}_{CA}}\] \[\Rightarrow \frac{k(\sqrt{2}T-{{T}_{C}})A}{a}=\frac{k({{T}_{C}}-T)A}{\sqrt{2}a}\] \[\Rightarrow \frac{{{T}_{C}}}{T}=\frac{3}{1+\sqrt{2}}\]You need to login to perform this action.
You will be redirected in
3 sec