Three rods of identical cross sectional area and made from the same metal form the sides of an equilateral triangle ABC. The points A and B are maintained at temperatures 3T and T respectively . In the steady state, the temperature of the point C is TC . Assuming that only heat conduction takes place, the value of TC/ T is equal to

QtAC=QtCB ;KA3T−TCl=KATC−Tl

Three rods of identical cross sectional area and made from the same metal form the sides of an equilateral triangle ABC. The points A and B are maintained at temperatures 3T and T respectively . In the steady state, the temperature of the point C is TC . Assuming that only heat conduction takes place, the value of TC/ T is equal to

QtAC=QtCB ;KA3T−TCl=KATC−Tl

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Three rods of identical cross sectional area and made from the same metal form the sides of an equilateral triangle ABC. The points A and B are maintained at temperatures $\sqrt{3} T$ and T respectively . In the steady state, the temperature of the point C is T_C . Assuming that only heat conduction takes place, the value of T_C/ T is equal to

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$\frac{1 - \sqrt{2}}{2}$

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

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

$\frac{1 - \sqrt{3}}{2}$

answer is A.

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Detailed Solution

${(\frac{Q}{t})}_{AC} = {(\frac{Q}{t})}_{CB}; \frac{KA (\sqrt{3} T - T_{C})}{l} = \frac{KA (T_{C} - T)}{l}$

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