Thermal conductivity of coppe is 9 times that of steel. As shown in figure the temperature difference between ends of copper and steel is `100^(@)C`. Find the temperature of their contact surface.

Options

A. `75^(@)C`
B. `67^(@)C`
C. `33^(@)C`
D. `25^(@)C`

Answer

A

Explanation

A = same cross - sectional area
`K_(c)=9K_(s)`
`T_(1)=100^(@)C`
`T_(2)=0^(@)C`

Suppose `T_(x)=` temperature of contact surface
In thermal equilibrium `H_(C)=H_(S)`
`:.(K_(c)A(T_(1)-T_(x)))/(L_(1))=(K_(s)A(T_(x)-T_(2)))/(L_(2))`
But `L_(1)=18` cm and `L_(2)=6` cm
`:.(9K_(s)(100-T_(x)))/(18)=(K_(s)(T_(x)-0))/(6)`
`:.3(100-T_(x))=T_(x)`
`:.300-3T_(x)=T_(x)`
`:.300=4T_(x)`
`:.T_(x)=(300)/(4)`
`:.T_(x)=75^(@)C`