Seven identical rods of matrical of thermal conductivity k are connected as shown in All the rod are of identical length l and cross sectional area `A` if the one end `b` is kept at `100^(@)C` and the other end is kept at `0^(@)C` The temperatures of the junctions `C,D` and `E(theta_(D)andtheta_(E))` be in the steady state
.

Options

A. `theta_(C)gt theta_(E) gt theta_(D)`
B. `theta_(E) =50^(@) C and theta_(D) = 37.5^(@)C`
C. `theta_(E) =50^(@)C,theta_(C)=62.5^(@)C and theta_(D) =37.5^(@)C`
D. `theta_(E) =50^(@)C,theta_(C)=60^(@)C and theta_(D) =40^(@)C`

Answer

A, C

Explanation

This problem can be solved like electric current problem
Let `R_(1) ,R_(2) ,R_(3), R_(4), R_(5), R_(6)` and `R_(7)` be the rates of heat flow through `AE, EB, AC, CD, CE,ED` and `DB` respectively
`R_(1) =R_(2) theta_(E) = 50^(@)C`
`R_(5) = R_(6) R_(3) =R_(4) + R_(5) =R_(7)`
`R_(4) + R_(6) =R_(7), (kA(theta_(c)-50))/(1) = (kA)/(1) (50 - theta_(D))`
`(kA)/(1) (100 -theta_(c)) = 100, 2theta_(c) - 2theta_(D) = 50rArr theta_(c) = 62.5^(@)C`
`theta_(D) = 37.5^(@)C, :. theta_(c) gt theta_(E) gt theta_(D)`
.