Three rods of lengths 20cm each and area of cross section `1cm^(2)` are joined to from a triangle ABC. The conductivities of the rods are `k_(AB)=50Js^(-1)m^(-1)C^(-1)` , `k_(BC)=200Js^(-1)m^(-1)C^(-1)` , and `k_(AC)=400Js^(-1)m^(-1)C^(-1)` . The junction A,B and C are maintained at `40^(@)C` , `80^(@)C` and `80^(@)C` respectively. Find the rate of heat flowing through the rods AB, AC and BC .

Answer

A

Explanation

`K_(AB)=50 J//m-s-^(@)C, Q_(A)=40^(@)C`
`K_(BC)=200 J//m-s-^(@)C, Q_B=80^(@)C`
`K_(CA)=400 j//m-s-^(@)C, Q_C=80^(@)C`
`Length =20cm=20xx10^_(-2)m`
`(a)(Q_(AB))/(t)=(K_(AB)A(theta_1-theta_2))/(l)`
`=(50xx1xx10^(-4)xx40)/(20xx10^(-2))=1 W.`
(b)`(Q_(AC))/(t)=(K_(AC)A(theta_A-theta_C))/(l)`
`=(400xx1xx10^(-4)xx40)/(20xx10^(-2))`
(Q_(BC))/(t)=(K_(BC)A(theta_B-thetaC))/(l)` ltbrge(200xx1xx10^(-4)xx0)/(20xx10^(-2))`.