Three metal rods made of copper, aluminium and brass, each `20 cm` long `4cm` in diameter, are placed end to end with aluminium between the other two. The free ends of copper and brass are maintained at `100` and `0^(@)C` respectively. Assume that the thermal conductivity of copper is twice that of aluminium and four times that of brass. The approximately equilibrium temperatures of the copper-aluminiu and aluminium-brass junctions are respectively.

Options

A. `68^(@)C` and `75^(@)C`
B. `75^(@)C` and `68^(@)C`
C. `57^(@)C` and `86^(@)C`
D. `86^(@)` and `57^(@)C`

Answer

D

Explanation

`R_(eq) = R_(1) +R_(2) +R_(3)`
where `R_(1) = (l)/((2k)A) , R_(2) =(l)/(kA), R_(3) (l)/(((k)/(2))A)`
`(100 -0)/(R_(eq)) = (100-T_(1))/(R_(1)) = (100-T_(2))/(R_(1)+R_(2)) = (T_(2)-0)/(R_(3))`