Question

Three identical rods of same metal are
connected as shown in figure. In steady state the
temperature T is
(1) 80°C
(3) 280°c
(2) 180°C
(4) 0°C​

Answer 1

Temperature at the junction would be 50°C

Three identical rods of same metal are connected as shown in figure.

here, heat flows through rod of temperature 70°C into both of the given rods ( 20°C and 60°C rods ).

so, heat lost by first rod = heat gained by 2nd and 3rd rod

⇒KA(70° - T)/l = KA(T - 20°)/l + KA(T - 60°)/l

[ here K is thermal conductivity, A is cross sectional area and l is length of each rod ]

⇒(70° - T) = (T - 20°) + (T - 60°)

⇒150° = 3T

⇒T = 50°

hence, temperature at the junction is 50°C.

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Answer 2

Answer:

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here, heat flows through rod of temperature 70°C into both of the given rods ( 20°C and 60°C rods ).

so, heat lost by first rod = heat gained by 2nd and 3rd rod

⇒KA(70° - T)/l = KA(T - 20°)/l + KA(T - 60°)/l

[ here K is thermal conductivity, A is cross sectional area and l is length of each rod ]

⇒(70° - T) = (T - 20°) + (T - 60°)

⇒150° = 3T

⇒T = 50°