Question

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.​

Answer 1

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>