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 $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1=0.02 {\mathrm{m}}^2, {\mathrm{K}}_1=79 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ and a brass bar$\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ 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. The temperature of the junction of the two bars is:

1.  $215 \mathrm{K}$

2.  $315 \mathrm{K}$

3.  $415 \mathrm{K}$

4.  $115 \mathrm{K}$

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 $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1 0.02 {\mathrm{m}}^2, {\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ 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. The heat current through the compound bar is:

1.  $916.1 \mathrm{W}$

2.  $826.1 \mathrm{W}$

3.  $926.1 \mathrm{W}$

4.  $726 \mathrm{W}$