Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are `K_1` and `K_2`. The temperature of the free ends of the first and second rods are maintained at `θ_1` and `θ_2` respectively. The temperature of the common junction is

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)` .