Two rods, one made of brass and the other made of copper, are joined end to end.

Question

Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is 0.300 m and the length of the copper section is 0.800 m . Each segment has cross-sectional area 0.00500 m2 . The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice-water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings.

What is the temperature of the point where the brass and copper segments are joined?

What mass of ice is melted in 5.00 min by the heat conducted by the composite rod?

Explanation / Answer

for Copper rate of heaT transfer is

PCu=kCuA(Tx-TCu)/LCu,

where Tx is temperature at intersection

and for Brass

PB=kBA(TB-Tx)/LB

PCu=PB (condition for steady state transfer)

ie.kCuA(Tx-TCu)/LCu=kBA(TB-Tx)/LB

solving the aBove equation we get

Tx=(kCuTCuLB+kBTBLCu)/(kCuLB+kBLCu)

putting all values

Tx=(385x273x0.3+109x373x0.8)/(385x0.3+109x0.8)

   = 316K

   = 43.0oC

P=A(TB-TCu)/)(LB/KB+LCu/KCu)

P=5.0x10-3(373-273)/(0.3/109+0.8/385)

   =103.51 J/Sec

since P=Q/t

Q=Pt=103.51x5x60 = 31054.5J (heat transfer in 5.3min)

also

Q=mL (where L for ice=334J/g)

m=Q/L=31054.5 / 334= 93 g of ice is melted into water by conduction of composite system

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