What is the temperature of the steel-copper junction in the steady state system show in Fig. `7(e).17`? Length of steel rod = 15.0 cm, length of the copper rod = 10.0 cm, temperature of the furnace `=300^(@)C`, temperature of 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 js^(-1) m^(-1) K^(-1)` and of copper `=3895 js^(-1) m^(-1) K^(-1)`).

Answer

`[44.4^(@)C]`

Explanation

Let `T .^(@)C` be the temperature of the steel-copper junction at steady state. So rate of heat conducted through steel = rate of heat conducted through copper
`:. (K_(s)A_(s)(T_(1)-T_(2)))/(x_(1))=(K_(c)A_(c)(T_(1)-T_(2)))/(x_(2))`
or `((50.2)xx(2A)xx(300-T))/((15.0xx10^(-2)))`
`=((385)xxAxx(T-0))/((10.0xx10^(-2)))`
On solving , we get `T=44.4^(@)C`