A bar of copper of length 75cm and a abr of steel of length 125cm are joined together end to end. Both are of circular cross section with diameter 2cm. The free ends of the copper and the steel bors are maintained at `100^(@)C` and 0^(@)C` respectively. The curved surface of the bors. are thermally insulated. What is the temperature of the coppe-steel junction? What is the amount of heat transmitted per unit time across the junction? Thermal conductivity of copper is `386Js^(-1)m^(-1)`^(@)C^(-1)` and that of steel is 46Js^(-1)m^(-1)`(@)C^(-1)

Explanation

The situation is shown in figure. Let the temperature at the junction be (theta) (on celsius scale). The same heat current passes through the copper and the steel rods. Thus,
`(DeltaQ)/(Deltat)=(K_(cu)A(100^(@)C-theta))/(75cm)=(K_(steel)Atheta)/(125cm)` . or, `(K_(cu)(100^(@)C-theta))/(75)=(K_(steel)theta)/(125)`. or, `(100^(@)C-theta)/(theta)=(75K_(steel))/(125K_(cu))=(3)/(5)xx(46)/(386)` . or, `theta=93^(@)C` . The rate of heat flow is
`(DeltaQ)/(Deltat)=(K_(steel)Atheta)/(125cm)` . `=((46Js^(-1)m^(-1)`^(@)C^(-1))(pixx1cm^(2))xx93^(@)C)/(125cm)` . `=1.07Js^(-1)` .