A bar of copper of length `75cm` and a bar 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 bars are maintained at `100^(@)C` and `0^(@)C` respectively. The curved surface of the bars are thermally insulated. What is the temperature of the copper-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)`

Answer

`[93^(@)C; 1.07 j//s]`

Explanation

Let `theta^(@)C` be the temperature of the junction, Fig. 7(e).22. As `(Delta Q//Delta t)` for both the rods is the same, therefore

`(Delta Q)/(Delta t)= (K_(cu)A(100^(@)-theta))/(0.75)= (K_(steel)A(theta-0^(@))/(1.25)`
`:. (386(100^(@)-theta))/(3)= (46theta)/(5)` or `theta= 93^(@)C`
Rate of heat flow `=(Delta Q)/(Delta t) =(K_(steel)Atheta)/(1.25)`
`=(46xxpi(0.1)^(2)xx93)/(1.25)= 1.07 j//s`