17.62 ° A long rod, insulated to prevent heat loss along its sides, is in perfec

Question

17.62 ° 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 cm*. 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 Boiling O O water Ice and COPPER STEEL water 1.00 m

Explanation / Answer

Given,

Heat passing through the copper rod, Q = K A dT/L = 385 x 0.0004 x 35/1 = 5.39 W

We know that heat will travel through the steel rod at the same rate

50.2 x 0.0004 x 65/L2 = 385 x 0.0004 x 35/1

50.2 x 65/L2 = 385 x 35

50.2 x 65/385 x 35 = L2

L2 = 0.242 m

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