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A steel bar 10.0 cm long is welded end t...

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)`.

Text Solution

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In the steady state, the two heat currents are equal. We have ltBrgt `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 an may be cancelled out.
Substituting `L_("steel")=0.100m,L_("copper")=0.200m`, and numerical values of K from the previous table, we find
`((50.2W//m.K)(100^(@)C-T))/(0.100m)=((385W//m.K)(T-0^(@)C))/(0.200m)`
Solving for T, we obtain `T=20.7^(@)C` ltBrgt 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)`
`becauseH_("steel")=15.9W`
`thereforeH_("copper")=15.9W`
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