Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K1,K2 and K3 respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K1,K2 and K3
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a
K1>K2>K3
b
K1:K3=3:5K1:K2=5:2,
c
K2:K3=2:5K1:K3=2:3,
d
K1
answer is C.
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Detailed Solution
Let cross-section area and length of each rod is A and l respectively. Then current (thermal) through each of them are equal.Using Q ˙=△TAKLSo 100−70AK1l=70−20AK2l=20−0AK3l⇒30K1=50K2=20K3 ⇒K1K3=23 and K2K3=25
Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K1,K2 and K3 respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K1,K2 and K3