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Two cylindrical rods have the same mass. One is made of silver (density = 10 500 kg/m3), and one is made of iron (density = 7860 kg/m3). Both rods conduct the same amount of heat per second when the same temperature difference is maintained across their ends. What is the ratio (silver-to-iron) of (a) the lengths and (b) the radii of these rods? Give your answers as numbers with no units
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Added Mon, 27 Jul '15
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Since the volume of a cylinder is V= pir^2h and have same conductivity,

(a) Since the volume and density are cubic units, the ratio is 10500/7860 = 175/131 = (hs/hi)^3

so the ratio is (175/131)^(1/3) = 1.1013

(b) For squared units (or for the radii ratio relative to the volume equation), it is

(175/131)^(2/3) = 1.213
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