What is the temperature of the steel - copper junction in the steady state of the system shown in Fig.11.15.

Length of the steel rod ` = 15.0 `cm, length of the copper reod ` = 10.0` cm, temperarure of the furnace ` = 300 ^(@) C`, temperature of the furnace ` = 300 ^(@) C` , temperature of the other end ` = 0^(@) C`. The are of cross section of the steel rod is twice that of the copper rod. ( Thermal conductivity of steel ` = 50.2 J s^(-1) m^(-1) K^(-1) ,` and of copper ` = 385 J s^(-1) m^(-1) K^(-1))`.

Explanation

Let T be the temperature of the steel-copper junction in the steady state.
`(K_(1) A_(1) (300 - T))/(L_(1)) = (K_(2) A_(2) (T- 0))/(L_(2))`
`(50.2 xx 2(300 - T))/(15) = (385T)/(10) ` which gives T = `44.4^(0)` C