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)`

Explanation

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

### Step 1: Define the Variables
- 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 both bars, \( d = 2 \, \text{cm} = 0.02 \, \text{m} \)
- Radius of both bars, \( r = \frac{d}{2} = 0.01 \, \text{m} \)
- Temperature at the free end of copper, \( T_c = 100^\circ C \)
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