What is the temperature of steel-copper jumction in the steady state of the system shown in fig. Length of the steel rod = 30.0 cm, length of the copper rod = 20.0 cm, temperature of the furnace = `300^(@)C`, temperature of cold 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) .^(@)C^(-1)` and of copper = `358 Js^(-1) m^(-1) .^(@)C^(-1)`.

Explanation

In the steady state, let T be the temperature of steel-copper junction.
Then heat flowing per second of steel = heat flowing per second of copper.
`(K_(1)A_(1)(300-T))/(x_1) = (K_(2)A_(2)(T-0))/(x_2) or (50.2 xx 2A_(2) xx (300-T))/(30) = (385 xxA_(2)(T-0))/(20)`
or, `100.4 (300-T) xx 20 = 385 T xx 30`
On solving , `T = 44.4^(@)C`