Q. Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles triangle 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
IIT JEEIIT JEE 1995Thermodynamics
Solution:
The diagramatic representation of the given problem is shown in figure. Since, T$_B > T_A$ the heat will flow from B to
A. Similarly, heat will also flow from B to C and C to A.
Applying the conduction formula
$\frac{\Delta Q}{\Delta t}=\frac{KA}{l}(\Delta T)$
To the sides CA and BC, we get
$\bigg(\frac{\Delta T}{\sqrt 2a}\bigg)_{CA} =\bigg(\frac{\Delta T}{a}\bigg)_{BC} \, \, \, \, \Rightarrow \, \, \, \frac{T_C-T}{\sqrt 2 a}=\frac{\sqrt 2 T -T_C}{a}$
$3T =T_C(\sqrt 2 +1) \, \, \, \Rightarrow \, \, \, \, \, \frac{T_C}{T}=\frac{3}{(\sqrt 2 +1)}$
