Properties Of Solids And Liquids Question 464
Question: Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles traingle ABC, right-angled at B. The points A and B are maintained at temperatures T and $ (\sqrt{2}) $ T respectively. In the steady state, the temperature of the point C is $ T _{c} $ . Assuming that only heat conduction takes place, $ T _{c}/T $ is
Options:
A) $ \frac{1}{2( \sqrt{2}-1 )} $
B) $ \frac{3}{\sqrt{2}+1} $
C) $ \frac{1}{\sqrt{3}( \sqrt{2}-1 )} $
D) $ \frac{1}{\sqrt{2}+1} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Heat flow from B to A,A to C and C to B (for steady state t condition, $ \Delta Q/\Delta t $ is same) Where $ \frac{\Delta Q}{\Delta t}=\frac{kA\Delta T}{\ell } $ For sides AC and CB $ {{( \frac{\Delta T}{\sqrt{2}a} )} _{AC}}={{( \frac{\Delta T}{a} )} _{CB}} $
$ \Rightarrow \frac{T-T _{C}}{\sqrt{2}A}=\frac{T _{C}-\sqrt{2}T}{a} $
$ \Rightarrow T-T _{C}=\sqrt{2}T _{C}-2T $
$ \Rightarrow 3T=T _{C}(\sqrt{2}+1)\Rightarrow \frac{T _{C}}{T}=\frac{3}{\sqrt{2}+1} $
