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 0.500 m and the length of the copper section is 0.700 m . Each segment has cross-sectional area 0.00700 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.

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

B.

What mass of ice is melted in 9.00 min by the heat conducted by the composite rod? Express your answer with the appropriate units.

Answer 1

Given: lFrom the questio we have ength of brass rod Lb = 0.500 m; length of copper rod Lc = 0.7 m; cross sectional area of both A = 0.00700 m^2

And the thermal conductivity of brass kb = 109 W/m-K; thermal conductivity of copper kc = 385 W/m-K

Heat conduction R = L/kA

Hence this is a series configuration so the net resistance is:

R = R1+ R2 = Lb/(kb*A) + Lc/(kc*A) = 0.500/(109*0.007) + 0.7/(385*0.007)

= 0.915 K/W

Here the temperature difference is ΔT = 100 K (boling point of water - melting point of water)

So heat flow rate dQ/dt = ΔT/R = 100/0.915

= 109.29 W

2. Hence heat supplied in 9 min ΔQ = 109.29 *9*60 = 59016.6 J

So the amount of ice melted with this heat is given by: m = ΔQ/L ;

where the latent heat capacity of water 'L' = 334000 J/Kg

Hence m = 59016.6/334000 = 0.18 Kg

1. Let the temperature of the joint be T we have:

dQ/dt = (T - 0)/R2 or T = (Lc/kc*A)*dQ/dt = 0.7*109.29/(385*0.007)

= 28.38 C