A copper rod of length 75 cm and an iron rod of length 125cm are joined together end to end . Both are of circular cross section with diameter 2 cm . The free ends of the copper and iron are maintained at `100^@C` and`0^@C` respectively . The surface of the bars are insulated thermally . The temperature of the copper -iron junction is [Thermal conductivity of the copper is `386.4 W//m-K ` and that of iron is `48.46W//m-K`].

Options

A. `100^@C`
B. `0^@C`
C. `93^@C`
D. `50^@C`

Answer

C

Explanation

Heat transfer takes place through conduction
`Q_(copper) = Q_(iron)`

`(K_(c)A_(c)(T_(c)-T))/(l_(c)) = (K_(i)A_(i)(T-T_(i)))/(l_(i))` `[because d_(c) = d_(i)]`
`implies` `(386.4(100 - T))/(75) = (48.46(T - 0))/(125)`
`implies` `5.152(100 - T) = 0.388 T` `implies` `5.540 T = 515.2`
`therefore` `T = 92.996 cong 93^(@)C`