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Question
The two rods shown in following figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.
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Solution
As the rods are connected in series, the rate of flow of heat will be same in both the cases.
ase 1:
Rate of flow of heat is given by `{dQ}/dt = (KA DeltaT)/l`
Rate of heat flow in rod P will be same as that in rod Q.
∴ `{K_pxxAxx(100 - 70)}/l ="(KQxx Axx(70 - 0))/l`
`⇒ 30 Kp = 70K_Q`
`⇒ K_Q = 3/7 K_p` ......................(1)
Case 2:
Again, the rate of flow of heat will be same in rod P and Q.
∴ `(K_QxxAxx(1100-T))/l = (K_pxxAxx(T - 0))/(l)`
`100 K_Q - K_QT = K_pT`
`100K_Q - K_QT = 70/30K_QT ` .........{using (i)}
`100- T = 7/3T`
`100 = 10/3 t`
`⇒ T = 30^circ C`
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