An iron bar of length 0.1 m and area of cross section 0.02 m2 and a brass bar of length 0.2 m and
area of cross section 0.02 m2 are soldered together end to end. The free ends of the iron bar and
brass bar are maintained at 100 oC and 0 oC respectively. The thermal conductivities of iron and
brass are 79 W m-1 K
-1 and 109 W m-1 K
-1
respectively. Calculate the temperature of the
iron – brass junction. Also find the heat current through the compound bar.
area of cross section 0.02 m2 are soldered together end to end. The free ends of the iron bar and
brass bar are maintained at 100 oC and 0 oC respectively. The thermal conductivities of iron and
brass are 79 W m-1 K
-1 and 109 W m-1 K
-1
respectively. Calculate the temperature of the
iron – brass junction. Also find the heat current through the compound bar.
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Explanation:
be the temperature of the junction of the two bars and A be the area of cross-section of each bar. <br> (i) Under steady state condition, the heat conducted per second through iron bar is equal to the heat conducted per second through brass bar, <br> i.e.,
<br> As,
, so <br>
...(i) <br> or
<br> or
<br> or
...(ii) <br>
. <br> (ii) Putting the value of
from (ii) in (i) we get <br>
<br>
...(iii) <br> If K is the equivalent thermal conductivity of the two bars, then <br>
...(iv) <br> From (iii) and (iv) , <br>
<br>
<br> (iii)
<br>