A bar of copper of length 75 cm and a bar of steel of length 125 cm are joined together end to end . Both are of circular cross - section with diameter 2 cm . The free ends of the copper and steel bars are maintained at `100^(@)C` and `0^(@)C` respectively . The surface of the bars are thermally insulted . What is the temperature of the copper - steel junction ? What is the heat transmitted per unit time across the junction ? Thermal conductivty of copper `9.2 xx 10^(-2) k cal m^(-1)``""^(@)C^(-1)s^(-1)` and that of steel is `1.1 xx 10^(-2)k cal m^(-1)s^(-1)``(@)C^(-1)`.

Explanation

To solve the problem, we need to find the temperature at the junction of the copper and steel bars and the heat transmitted per unit time across the junction.

### Step 1: Identify the Given Data
- Length of copper bar, \( L_c = 75 \, \text{cm} = 0.75 \, \text{m} \)
- Length of steel bar, \( L_s = 125 \, \text{cm} = 1.25 \, \text{m} \)
- Diameter of the bars, \( d = 2 \, \text{cm} = 0.02 \, \text{m} \)
- Temperature at the free end of copper, \( T_c = 100^\circ C \)
- Temperature at the free end of steel, \( T_s = 0^\circ C \)
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