Three rods `A, B` and `C` of the same length and cross- sectional area are joined in series as shown. The temperature at the junction of `A` and `B`, in equilibriu, is

Options

A. `74^(@)C`
B. `116^(@)C`
C. `156^(@)C`
D. `148^(@)C`

Answer

B

Explanation

(2) `R prop (1)/("Thermal conductivity")`
`R_(1) = R, R_(2) = (R )/(2), R_(3) = (2 R)/(3)`
In series, heat current is same.
`i = (200 - theta_(1))/(R_(1)) = (theta_(1) - theta_(2))/(R_(2)) = (theta_(2) - 18)/(R_(3))`
`(200 - theta_(1))/(R_(1)) = (theta_(1) - theta_(2))/((R//2)) = (theta_(2) - 18)/((2 R //3))`
`200 - theta_(1) = 2 theta_(1) - 2 theta_(2) = (3 theta_(2) - 54)/(2)`
`200 - theta_(1) = 2 theta_(1) - 2 theta_(2) implies 3 theta_(1) - 2 theta_(2) = 200`
`2 theta_(1) - 2 theta_(2) = (2 theta_(2) - 54)/(2) implies 4 theta_(1) - 7 theta_(2) = - 54`
Solving (i) and (ii), `theta_(1) = 116^(@)C`