Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be :

Question

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be : (A) (3(K1 + K2)/2) (B) K1 + K2 (C) 2( K1 + K2) (D) (K1 + K2/2)

Tardigrade Admin · Accepted Answer

R 1=( d / k 1 A ) R 2= d K 2 A operatornameReq=( R 1 R 2/ R 1+ R 2) ( d / keq (2 A ))=((( d / k 1 A ))(( d / k 2 A ))/ A )((1/ k 1)+(1/ k 2)) (1/2 keq )=((1/ k 1 k 2)/( k 1+ k 2) k 1 k 2)=(1/ k 1+ k 2) keq =( k 1+ k 2/2)

Q. Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be :

$\frac{3 ( K _{1} + K _{2} )}{2}$

$K_{1} + K_{2}$

$2 (K_{1} + K_{2})$

$\frac{K _{1} + K _{2}}{2}$

Q. Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1​ and K2​. The thermal conductivity of the composite rod will be :

23(K1​+K2​)​

K1​+K2​

2(K1​+K2​)

2K1​+K2​​

R1​=k1​Ad​ R2​=dK2​A Req=R1​+R2​R1​R2​​ keq(2A)d​=A(k1​Ad​)(k2​Ad​)​(k1​1​+k2​1​) 2keq1​=k1​k2​k1​+k2​​k1​k2​1​​=k1​+k2​1​ keq=2k1​+k2​​

Q. Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be :

$\frac{3 ( K _{1} + K _{2} )}{2}$

$K_{1} + K_{2}$

$2 (K_{1} + K_{2})$

$\frac{K _{1} + K _{2}}{2}$