A bar of length 30 cm of uniform cross-section of 5 `cm^2` consists of two halved `AB` of copper and BC of iron welded together at B. The end A is maintained at 200°C and the end C at `0^(@)` C and the sides are thermally insulated. Find the rate of flow of heat along the bar when the steady state is reached. Thermal conductivities are copper `378 "Wm"^(-1) "K"^(-1)` and iron 50.4 `"Wm"^(-1) "K"^(-1)` (Fig. 11.12)

Explanation

Thermal resistance `= (l)/( AK)`, where `l` is the length of the bar, A its area of cross-section and `K` is coefficient of thermal conductivity.
Thermal resistance of copper R `= (15 xx 10^(-2) )/( 5 xx 10^(-4) xx 378 ) = 0.793 "KW"^(-1)`
Thermal resistance of iron `R_2 = (15 xx 10^(-2) )/( 5 xx 10^(-4) xx 50.4 ) = 5.95 "KW"^(-1)`
The two bars are in series so total thermal resistance
`= R = R_1 + R_2 = 0.793 + 5.95 = 6.743`
Rate of heat flow `= ("Temperature difference between the two ends")/(" Total thermal resistance")`
`= (200-0)/( 6.743 ) = 29.67 "J/S"`