Question

Three rods of identical cross-sectional area and made from the same metal form 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. Assuming that only heat conduction takes place, temperature of point C will be –

• A. $\frac{3T}{\sqrt{2} + 1}$
• B. $\frac{T}{\sqrt{2} + 1}$
• C. $\frac{T}{\sqrt{3}(\sqrt{2} - 1)}$
• D. $\frac{T}{\sqrt{2} - 1}$

Answer 1

Answer: (A)

$\frac{3T}{\sqrt{2} + 1}$

Answer 2

$\frac{kA(\sqrt{2}T - \theta)}{\mathcal{l}}$ = $\frac{kA(\theta - T)}{\sqrt{2}\mathcal{l}}$

Ž 2T – $\sqrt{2}$q = q – T

3T = $(1 + \sqrt{2})$ q

q = $\frac{3T}{1 + \sqrt{2}}$