(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 [T.- T, dQ = 2Lk dt In(b/a) Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 27rL. (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? T. Figure P19.45

(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 [T.- T, dQ = 2Lk dt In(b/a) Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 27rL. (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? T. Figure P19.45

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

(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
[T.- T,
dQ
= 2Lk
dt
In(b/a)
Suggestions: The temperature gradient is dT/dr. A radial
energy current passes through a concentric cylinder of area
27rL. (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?
T.
Figure P19.45

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