Two rods, one made of brass and the other made of copper, are joined end to end.
ID: 3160963 • Letter: T
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 0.400m and the length of the copper section is 0.900m. Each segment has cross-sectional area 0.00700 m^2. 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 7.00 min by the heat conducted by the composite rod? (Please, show all the steps)
Explanation / Answer
Thermal conductivity of brass and copper are 109 W/m K and 386 W /m K
let the tempertaure of the junction be T
Heat conducted through brass = Heat conducted through copper
k1*A1* dT/dx = k2*A1*dT/dx
109*0.007 * (373 - T ) / (0.4) = 386 * 0.007 * ( T-273) / 0.9
t = 311.85 K
temperature in oC = 311.85 - 273 = 38.85 oC
b) heat conducted = 109*0.007*(373 - 311.85) / 0.4
= 116.643 W
mass of ice melted = Q/L
= 116.643*(7*60) / (333.55*1000)
= 0.147 kg
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