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 \(\left(L_{1}   =   0 . 1   m ,   A_{1} =  0 . 02   m^{2} ,   K_{1}   =   79   W   m^{- 1}   K^{- 1}\right)\) and a brass bar \(\left(L_{2}   =   0 . 1   m ,   A_{2}   =   0 . 02   m^{2} ,   K_{2}   =   109   W   m^{- 1}   K^{- 1}\right)\) 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 temperature of the junction of the two bars is:

1.  215 K

2. 315 K

3. 415 K

4.115 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:

1. \(94.6~\text{W m}^{-1}\text{K}^{-1}\)

An iron bar \(\left(L_{1} = 0 . 1 ~ \text{m},   A_{1} =  0 . 02 ~\text{m}^{2}, K_{1} = 79~\text{W m}^{- 1} \text{K}^{- 1}\right)\) 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