Two metal rods, one silver and the other gold, are attached to each other. The f

Question

Two metal rods, one silver and the other gold, are attached to each other. The free end of the silver rod is connected to a steam chamber, with a temperature of 100°C, and the free end of the gold rod to an ice water bath, with a temperature of 0°C. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. How much heat flows through the two rods in 60 s? The thermal conductivity of silver is 417 W/(m·K), and that of gold is 291 W/(m·K). No heat is exchanged between the rods and the surroundings, except at the ends.

Work Please!

Explanation / Answer

dQ/dt = k*A*dT/L

From one end of the silver rod to the other end

dQ/dt = 417*A*(100-T)/L.....(1)

in case of Gold

dQ/dt = 291*T*A/L...........(2)

(2)= (1)

291*T = 417*(100-T)

T = 417*100/(291+417) = 58.9 degree celsius

then dQ/dt = 417*(100-58.9)*0.02*0.02/0.05 = 137.1

dQ = 137.1*60 = 8226.576 J

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