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 °C, temperature of the other end = 0 °C. The area of the cross section of the steel rod is twice that of the copper rod.

(Thermal conductivity of steel = $50.2 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$; and of copper = $385 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$).

1.  $44.4 °\mathrm{C}$

2.  $44.4 \mathrm{K}$

3.  $54.4 °\mathrm{C}$

4.  $54.4 \mathrm{K}$

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 $\left({\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ 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 and the  The equivalent thermal conductivity of the compound bar is:

1.  $94.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

2.  $93.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

3.  $81.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

4.  $91.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

An iron bar \((L_{1}   =   0 . 1 ~ \text m ,   A_{1} =  0 . 02 ~\text   m^{2} , \) \( K_{1}   =   79   W   m^{- 1}   K^{- 1})\) and a brass bar \((L_{2}   =   0 . 1   m ,   A_{2}   =   0 . 02   m^{2} , \) \(  K_{2}   =   109   W   m^{- 1}   K^{- 1})\) 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. The heat current through the compound bar is:

1.  \(916.1\) W

2.  \(826.1\) W

3.  \(926.1\) W

4.  \(726\) W