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# Three rods of identical area of cross-section 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 $\sqrt{2}\mathrm{T}$, respectively. In the steady state, the temperature of the point C is TC. Assuming that only heat conduction takes place, TC/T is equal to

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a
1(2+1)
b
3(2+1)
c
12(2−1)
d
13(2−1)
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detailed solution

Correct option is B

∵TB>TA⇒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 samei.e. QtBC=QtCA      ⇒k2T−TCAa=kTC−TA2a      ⇒TCT=31+2

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