Question

In the question number of `45`, the equivalent thermal conductivity of the compound bar is
A. `(K_(1)K_(2))/(K_(1)+K_(2))`
B. `(2K_(1)K_(2))/(K_(1)+K_(2))`
C. `(K_(1))/(K_(1)+K_(2))`
D. `(K_(2))/(K_(1)+K_(2))`

Answer 1

Correct Answer - B
Let K be thermal conductivity of the temperature bar.
Heat current through the compound bar of length `2L` is `H = (KA(T_(1) - T_(2)))/(2L)`
At steady state, `H = H_(1) = H_(2)`
`:. (KA(T_(1) - T_(2)))/(2L) = (K_(1)A(T_(1) - T_(0)))/(L) "…..."(ii)`
Substituting the value of `T_(0)` Eq (i) in (ii), we get
`(K(T_(1)-T_(2)))/(2)= K_(1)[T_(1) - ((K_(1)T_(1) + K_(2)T_(2))/((K_(1)+K_(2))))] = (K_(1)K_(2)(T_(1)-T_(2)))/((K_(1)+K_(2)))`
`rArr = (2K_(1)K_(2))/(K_(1)+K_(2))`