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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.
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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