Three bars of equal lengths and equal area of cross-section are connected in series fig. their thermal conducitives are in the ratio `2:3:4`. If at the steady state the open ends of the first and the last bars are at temperature `200^(@)C` and `20^(@)C` respectively, find the temperature of both the junctions.
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Explanation

Let the temperature of the junction B and C be `theta_(1)` and `theta_(2)`, respectively. In the steady state, the rate of flow of heat through all rods will be the same.
Therefore, Heat transfer `H = (2K) A(200-theta_(1))/L`
(4K)A(theta_(1)-theta_(2))/L= (3K) A(theta_(2) - 18)/L)`
or `2(200-theta_(1)) = 4(theta_(1)-theta_(2)) = 3(theta_(2)-18)`
Solving, `theta_(1)=116^(@)`C, `theta_(2)=74^(@)`C