Question

A steel bar 10.0 cm long is welded end to end to a copper bae 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 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)`.

Answer 1

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))`
Substituting, `L_(steel)` = 0.10m, `L_(copper)` = 0.200m
`K_(steel) = 50.2Wm^(-1)K^(-1)`,
`K_(copper) = 385 Wm^(-1)K^(-1)`
Also, both rods are same area.
So, `((50.2)(100^(@)C-T))/(0.100) = ((385)(T-0^(@)C))/(0.100)`
`H_(steel) = 796.17W`
`therefore` `H_(steel) = H_(copper)`
`therefore` `H_(copper)` = 796.17W