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)`).

Explanation

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`