A hot reservoir with a temperature of 687 K is 0.58 m away from a cold reservoir
ID: 1511281 • Letter: A
Question
A hot reservoir with a temperature of 687 K is 0.58 m away from a cold reservoir with a temperature of 358 K. The two reservoirs are insulated from each other except for a rod of brass (k = 109 W/m-K) that has a cross-sectional area of 0.058 m2. The entire system is allowed to reach a steady-state condition. 1) How much energy is transferred by heat between the hot reservoir and the cold reservoir in ten minutes? J Submit 2) Assume that you need to transfer 4155660 J of energy in ten minutes between the two reservoirs. To enhance the rate of energy transfer, a steel rod (k = 43 W/m-K) of the same length is added between the two reservoirs. What should the cross-sectional area of the steel rod be in order to achieve the proper rate of energy transfer?
Explanation / Answer
1) T1 = 687 K , T2 = 358 K , L = 0.58 m , A =0.058 m^2, K =109 W/m .K , t = 10 min = 10*60 s
Q/t = KA(T1 -T2)/L
Q/(10*60) = 109*0.058*(687 -358)/0.58
Q = 2151660 J
2) Q = 4155660 J , K = 43 W/m.K, t =10 min , L = 0.58 m
4155660/(10*60) = 43*A*(687 - 358)/0.58
A = 0.284 m^2
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