A heat-conducting rod is constructed with a 0.15 m length of alloy A and a 0.40

Question

A heat-conducting rod is constructed with a 0.15 m length of alloy A and a 0.40 m length of alloy B, joined end-to-end.
Both pieces have cross-section areas of 0.002 m2. The thermal conductivity of alloy B is known to be 1.8 times as great
as that for alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C and the other end is maintained
at an unknown temperature. The temperature at the junction of the alloys is 40°C. The heat current in the rod is 56 W.
14) In Situation 16.1, the temperature of the end of the rod in alloy B, in °C, is closest to: 14)
A) 84 B) 96 C) 88 D) 92 E) 80
Answer: A
15) In Situation 16.1, the thermal conductivity of alloy A is closest to: 15)
A) 120 W/m · K
B) 125 W/m · K
C) 140 W/m · K
D) 130 W/m · K
E) 135 W/m · K

Explanation / Answer

Let the thermal conductivity of alloy A = K

then heat current , q = KA ( T1 -T2 ) /L

=>56 = K * ( 0.002) *(40 - 10 )/ 0.15

=> 56 = K* (0.4 )

=> K= 140 W/m .K ............ans (15---C )

therefore thermal conductivty of alloy B = 1.8 * 140 = 252 W/m .K

the heat current is same in alloy B = 56W

56 = (252) * ( 0.002) *(T - 40 )/ 0.4 , where T is the temperature at the end of B .

=> 44.4 = (T -40 )

=> T = 84. 44 0C ..........answer (14 --A )

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