A heat conducting rod,1.60 m long,is made of an aluminum section,0.90 m long,and a copper section,0.70 m long.Both sections have a cross-sectional area of 0.0004 m².The aluminum end and the copper end are maintained at temperatures of 30°C and 170°C,respectively.The thermal conductivities of aluminum and copper are 205 and 385 W/m ∙ K,respectively.The rate at which heat is conducted in the rod is closest to:

Question

Quizplus · Accepted Answer

The rate of heat conduction is given by:Q/t = kA(dT/dx)where:Q/t is the rate of heat conductionk is the thermal conductivityA is the cross-sectional areadT/dx is the temperature gradientThe temperature gradient is:dT/dx = (T2 - T1)/Lwhere:T2 is the temperature at the hot endT1 is the temperature at the cold endL is the length of the rodThe rate of heat conduction is then:Q/t = kA(T2 - T1)/LFor the aluminum section:Q/t = (205 W/m ∙ K)(0.0004 m2)(170°C - 30°C)/0.90 m = 5.78 WFor the copper section:Q/t = (385 W/m ∙ K)(0.0004 m2)(170°C - 30°C)/0.70 m = 8.22 WThe total rate of heat conduction is:Q/t = 5.78 W + 8.22 W = 14.0 WThe closest answer choice is A) 9.0 W.

A Heat Conducting Rod,1