Two identical rods AC and CB made of two different metals having thermal conductivities in the ratio `2 : 3` are kept in contact with each other at the end C as shown in the figure.A is at `100^(@)C` and B is at `25^(@)`C.Then the junction C is at

Options

A. `55^(@)C`
B. `60^(@)C`
C. `75^(@)C`
D. `50^(@)C`

Answer

A

Explanation

For conduction of heat , `Q = KA (theta_(1) - theta_(2)t)/(d)`
Let temperature of junctiom = `theta`
`therefore K_(1) (100 - theta) = K_(2)(theta - 25)`
or `(K_(1))/(K_(2)) = (theta - 25)/(100 - theta)` or `(2/3) = (theta - 25)/(100 - theta)`
or `3theta - 75 = 200 - 2theta or 5 theta = 275 or theta = 55^(@)C`.