Final answer:
The total rate of heat flow through the stainless steel and copper bars is 924.24 W.
Step-by-step explanation:
The rate of heat flow through the bars can be calculated by equating the rate of conduction through the stainless steel bar to the rate of conduction through the copper bar. Since both bars are perfectly insulated on their sides, all the heat that enters the stainless steel bar from the steam will flow through the stainless steel bar and then through the copper bar to the ice. The thermal conductivity of stainless steel is 16.0 W/m·°C, and the thermal conductivity of copper is 400.0 W/m·°C.
Calculations:
The cross-sectional area of the bars is A = (1.9000000000000001 cm)2 = 0.0361 cm2 = 0.000361 m2.
The temperature difference between the steam and ice is ΔT = 100 °C - 0 °C = 100 °C.
The length of the stainless steel bar is Lstainless steel = 8.4 cm = 0.084 m.
The length of the copper bar is Lcopper = 16.8 cm = 0.168 m.
The rate of conduction through the stainless steel bar can be calculated using the formula:
Qstainless steel = kstainless steel × A × (ΔT / Lstainless steel)
Qstainless steel = 16.0 W/m·°C × 0.000361 m2 × (100 °C / 0.084 m)
Qstainless steel = 68.88 W.
The rate of conduction through the copper bar can be calculated using the formula:
Qcopper = kcopper × A × (ΔT / Lcopper)
Qcopper = 400.0 W/m·°C × 0.000361 m2 × (100 °C / 0.168 m)
Qcopper = 855.36 W.
Since the rate of conduction through the stainless steel bar is equal to the rate of conduction through the copper bar, the total rate of heat flow through the bars is:
Total rate of heat flow = Qstainless steel + Qcopper
Total rate of heat flow = 68.88 W + 855.36 W
Total rate of heat flow = 924.24 W