Three metal rods of the same material and identical in all respect are joined as shown in the figure. The temperatures at the ends are maintained as indicated. Assuming no loss of heat from the curved surface of the rods, the temperature at the junction X would be

Options

A. `45^(@)C`
B. `60^(@)C`
C. `30^(@)C`
D. `20^(@)C`

Answer

B

Explanation

Let T be the temperature at the junction,
Let L and A be the length and area of cross-section of each rod respectively.
`:.` Heat current from `Y` to X is
`H_(1) = (KA(90^(@)C-T))/(L)`
Heat current from Z to W is
`H_(2) = (KA(90^(@)C-T))/(L)`
Heat current from X to W is
`H_(3) = (KA(T - 0^(@)C))/(L)`
At the junction X,
`H_(1) + H_(2) = H_(3)`,
`:. 90^(2)C - T + 90^(@)C - T = T`
or `3T = 180^(2)C` or `T = 60^(@)C`