(a) The inside of a hollow cylinder is maintained at a tem- perature T, and the outside is at a lower temperature, T (Fig. P19.45). The wall of the cylinder has a thermal conduc- tivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is dQ dt = 2mLk [T.-T] In(b/a) Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2TTL. (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 insulat- ing material 6.00 cm in thickness and having a thermal conductivity of 4.00 x 10-5 cal/s cm. °C. A heater must maintain the interior temperature at 25.0°C while the out- side temperature is -35.0°C. What power must be supplied to the heater? L

(a) The inside of a hollow cylinder is maintained at a tem- perature T, and the outside is at a lower temperature, T (Fig. P19.45). The wall of the cylinder has a thermal conduc- tivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is dQ dt = 2mLk [T.-T] In(b/a) Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2TTL. (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 insulat- ing material 6.00 cm in thickness and having a thermal conductivity of 4.00 x 10-5 cal/s cm. °C. A heater must maintain the interior temperature at 25.0°C while the out- side temperature is -35.0°C. What power must be supplied to the heater? L

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 45CP: (a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower...

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(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 conduction from the inner surface to the outer surface in the radial direction is dQdt=2Lk[TaTbln(b/a)] Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2rL. (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 4.00 105 cal/s cm C. A heater must maintain the interior temperature at 25.0C while the outside temperature is 35.0C. What power must be supplied to the heater? Figure P19.45
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