The ends of a thin bar are maintained at different temperatures. The temperature

Question

The ends of a thin bar are maintained at different temperatures. The temperature of the cooler end is 8degree C, while the temperature at a point 0.12 m from the cooler end is 23degree C and the temperature of the warmer end is 43degree C. Assuming that heat flows only along the length of the bar (the sides are insulated), find the length of the bar. A copper rod has a length of 1.7 m and a cross-sectional area of 3.9 x 10^-4 m^2. One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod. As an aid in working this problem, consult Concept Simulation 13.1.

Explanation / Answer

7)

Start at the cooler end

Temp difference between cool end and point 0.12m away is 15 degrees. So we can use an increse of 8 degrees for every 0.12m increment.

Diff. between hot end and 0.12m point is 20 degrees, hence-:

20 / 15 = 1.333.
1.333 x 0.12m = 0.16 metres.

Then we just add them up.
0.16 + 0.12 = 0.28 m = 28 cm

8)

thermal conductivity of Copper is 401 W/mK

heat of fusion of ice is 334 kJ/kg

Thermal Conductivity
P = K x T x A / d
K is thermal conductivity in W/mK
P is power in watts transferred through the material
K is thermal conductivity of the material in W/mK
T is change in temperature across the material
A is cross-sectional area in m²
d is thickness in m

Take a time period of 1 second
P = K x T x A / d
P = 401 W/mK x 100 x (3.9 x 10^-4)/1.7
P = 9.20 watts, or 9.20 joules per second.

how much ice does this melt
9.20 = 334000 J/kg x m
m = 2.754 x 10^-5 kg = 27.54 mg

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