(a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower temperature, Tb (Fig. P19.45). The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy
Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2πrL. (b) The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of 35.0 m and an inner radius of 2.50 m. Its walls are lined with an insulating material 6.00 cm in thickness and having a thermal conductivity of 4.00 × 10−5 cal/s · cm · °C. A heater must maintain the interior temperature at 25.0°C while the outside temperature is −35.0°C. What power must be supplied to the heater?
Figure P19.45
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Physics for Scientists and Engineers with Modern Physics
- An aluminum rod 0.500 m in length and with a cross sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 3(H) K. (a) If one-halt of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool, (b) If the circular surface of the upper end of the rod is maintained at 300 K. what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 YV/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)arrow_forwardA brass ring of diameter 10.00 cm at 20.00C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.00C. Assuming the average coefficients of thermal expansion are constant for brass and aluminum, (a) to what temperature must this combination be cooled to separate them? Is this attainable? (b) What if the aluminum rod is 10.02 cm in diameterarrow_forwardGiven that a homogenous material will have the same expansivity properties in every direction. Hence such an object changes its overall size upon heating, but not its shape., a) find the new diameter of a solid brass sphere of radius 0.9535 m when its temperature rises 200°C. b) If the sphere of a) were hollow instead, with inner diameter 0.8535 m, what would be the new inside diameter for the same temperature rise? (the coefficient of linear expansion for brass is 1.93 x 10^(-5)/°C)arrow_forward
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