What is the temperature of the steel-copper junction in the steady-state of the system shown in the figure? The length of the steel rod = \(15.0\) cm, length of the copper rod = \(10.0\) cm, temperature of the furnace = \(300^{\circ}\text{C}\), temperature of the other end = \(0^{\circ}\text{C}\). The area of the cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel = \(50.2 ~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1};\) and of copper \(= 385~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1})\).

         

An iron bar
\(\left(L_{1}=0.1 \text{m} ,   A_{1}=0.02~\text{m}^{2} ,   K_{1}=79~\text{Wm}^{- 1}   \text{K}^{-1}\right)\) and a brass bar
\(\left(L_{2}=0.1~\text{m} , A_{2}=0.02~\text{m}^{2} , K_{2}=109~\text{Wm}^{- 1}  \text{K}^{- 1}\right)\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at \(373~ \text{K}\) and \(273~ \text{K}\) respectively. The temperature of the junction of the two bars is:
             

1. \(215~ \text{K}\) 
2. \(315~ \text{K}\) 
3. \(415~ \text{K}\) 
4. \(115~ \text{K}\)

An iron bar \(K_1 = 79~\text{W m}^{-1}\text{K}^{-1}\) and a brass bar \(K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at \(373\) K and \(273\) K respectively. Then the equivalent thermal conductivity of the compound bar is:

An iron bar \(\left(L_{1} = 0 . 1 ~ \text{m},   A_{1} =  0 . 02 ~\text{m}^{2}, K_{1} = 79~\text{W m}^{- 1} \text{K}^{- 1}\right)\) and a brass bar \(\left(L_{2}= 0 . 1 ~\text{m}, A_2 = 0.02~\text{m}^2, K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\right)\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at \(373\) K and \(273\) K respectively. The heat current through the compound bar is:

1. \(916.1\) W
2. \(826.1\) W
3. \(926.1\) W
4. \(726\) W