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What is the temperature of the steel-copper junction is the steady state of the system shown in figure. Length of the steel rod = 15.0 cm, length of the copper rod = 10.0 cm, temperature of the furnace =300^(@)C, temperature of the other end =0^(@)C. The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel =50.2" Js"^(-1)m^(-1)K^(-1), and copper =385" Js"^(-1)m^(-1)KJ^(-1)). |
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Answer» Solution :Temperature of furnance `T_(1)=300^(@)C` Temperature of ice box `T_(2)=0^(@)C` Temperature of junction `=T^(@)C` By taking sign 1 for steel and 2 for copper, Thermal CONDUCTIVITY of steel `K_(1)=50.2" Js"^(-1)m^(-1)K^(-1)`, length `L_(1)=15` cm Thermal conductivity of copper `K_(2)=385" Js"^(-1)K^(-1)`, length `L_(2)=10` cm HEAT current joining in steel and copper is same under thermal study state `H_(1)=H_(2)` `:.(K_(1)A_(1)(T_(1)-T))/(L_(1))=(K_(2)A_(2)(T-T_(2)))/(L_(2))` `:.(50.2xx2A_(2)(300-T))/(0.15)=(385xxA_(2)(T-0))/(0.10)` `:.(50.2xx2xx(300-T))/(3)=(385T)/(2)` `:.200.8(300-T)=1155T` `:.60240-200.8T=1155T` `:.60240=1355.8T` `:.T=(60240)/(1355.8)` `:.T=44.43^(@)C` |
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