Metal rods X and Y of identical cross-sectional area, have lengths 60 cm and 30 cm respectively. They are made of metals of thermal conductivities `lambda_(x)` and `lambda_(y)`. They are well-lagged and joined end-to-end as shown in the figure-4.43. One end of X is maintained at `100^(@)C` and the opposite end of Y is maintained at `0^(@)C`. When steady conditions have been .reached, the temperature of the junction is found to be `25^(@)C`.
What is the value of `(lambda_(x))/(lambda_(y))` ?

Options

A. `(1)/(6)`
B. `(2)/(3)`
C. `(25)/(24)`
D. `(3)/(2)`

Answer

B

Explanation

We use for conduction rate
`(lambda_(x)xxA(100 - 25) /(60) =(lambda _(y) A(25 - 0))/(30)`
`rArr``(lambda_(x))/(lambda_(y)) =(25)/(30)xx(60)/(75) =(2)/(3)`