A steel bar 10.0 cm long is welded end to end to a copper bar 20.0 cm long. Both bars are insulated perfectly on their sides . Each bar has a separate cross-section, 2.00 cm on a side . The free end of the steel bar is maintained at `100^(@)C` by placing it in contact with steam and free end of the copper bar is maintained at `0^(@)C` by placing it in contact with ice . find the temperature at the junction of the two bars and the total rate of heat flow . thermal conductivity of steel `= 50.2 Wm^(-1)K^(-1)`.thermal conductivity of copper `=385 Wm^(-1)K^(-1)`.

Explanation

In the steady state , the two heat currents are equal ,We have
`H_(steel)=(K_(steel)A(100"^(@)C-T))/(L_(steel))` and `H_(copper)=(K_(copper)A(T-0"^(@)C))/(L_(copper))`
The areas A are equal and may be cancelled out.
Substituting `L_(steel)`=0.100m ,`L_(copper)`=0.200m , and numerical values of k from the previous table we find
`((50.2 W//m.K)(100"^(@)C-T))/(0.100m)` =`((385 W//m.K)(T-0"^(@)C))/(0.200m)`
Solving for T we obtain `T=20.7"^(@)C`
We can find the total heat current by substituting this value for T
`H_(steel)=((50.2W//m.k)(0.0200m^2)(100"^(@)C-20.7"^(@)C))/(0.100m)`
`H_(steel)=15.9W`
`H_(steel)=H_(copper)`
`H_(copper)`=15.9W