The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.



Let’s take first condition –


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Since, rods are connected in series, rate of heat flow remains constant.


= = constant


Where


∆T = is change in temperature between the two sides of the rods.


A= Area of cross section of the rods


K = thermal conductivity of the rods


L = length of the rod


Hence


=


Where ,



KA , KB are thermal conductivity of rod A and B


⇒ 30 KA = 70 KB ……………………………(1)


Now, in second condition, the rods are interchanged as shown in fig below –


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Let x°C be the unknown temperature of the junction AB


Now, since rate of heat flow remains constant-


=


That gives


100B - xB = A x


Substituting for A from(1) and solving the above equation


100 = x +x


⇒


x = 30°C


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