A steel bar 10.0 cm long is welded end to end to a copper bae 20.0 cm long. Both bars are insulated perfectly on their sides . Each bar has a separate cross-section, 2.00 cm on a side . The free end of the steel bar is maintained at `100^(@)C` by placing it in contact with ice . find the temperature at the junction of the two bars and the total rate of heat flow . thermal conductivity of steel `= 50.2 Wm^(-1)K^(-1)`.thermal conductivity of copper `=385 Wm^(-1)K^(-1)`.

Explanation

To solve the problem, we need to find the temperature at the junction of the steel and copper bars and the total rate of heat flow. We will use the concept of thermal conductivity and the formula for heat transfer through a material.

### Step 1: Identify the given values
- Length of steel bar, \( L_s = 10.0 \, \text{cm} = 0.1 \, \text{m} \)
- Length of copper bar, \( L_c = 20.0 \, \text{cm} = 0.2 \, \text{m} \)
- Thermal conductivity of steel, \( k_s = 50.2 \, \text{W/m·K} \)
- Thermal conductivity of copper, \( k_c = 385 \, \text{W/m·K} \)
- Temperature at the free end of the steel bar, \( T_s = 100^\circ C \)
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