A long rod, insulated to prevent heat loss along its sides, is in perfect therma

Question

A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice-water mixture at the other (Fig E17.62). The rod consists of a 1.00-m section of copper (one end in boiling water) joined end to end to a length L2 of steel (one end in the ice-water mixture). Both sections of the rod have cross-sectional areas of 4.00 cm2. The temperature of the copper-steel junction is 65.0° C after a steady state has been set up. (a) How much heat per second flows from the boiling water to the ice-water mixture? (b) What is the length L2 of the steel section? Figure E17.62 Insulation 65.0°C olling lce and COPPER STEEL water O water 1.00 m

Explanation / Answer

a)Given,

L = 1 m ; A = 4 cm^2 ; theta = 65 deg

P = k A dt/dx

P = 385 x 4 (100 - 65)/1 = 5.39 W

Hence, P = 5.39 W

b)5.39 = 50.2 x 4 x 10^-4 x 65/L2

L2 = 0.242

Hence, L2 = 0.242 m

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