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 $$2T$$, 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

Question

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 $$2T$$, 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

Infinity Learn · Accepted Answer

∵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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