Physics for Scientists and Engineers
Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 19, Problem 45CP

(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

d Q d t = 2 π L k [ T a T b ln ( b / a ) ]

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

Chapter 19, 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 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 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 Figure P19.45
A spherical shell has inner radius 3.00 cm and outer radius 7.00 cm. It is made of material with thermal conductivity k = 0.800 W/m - °C. The interior is maintained at tempera- ture 5°C and the exterior at 40°C. After an interval of time, the shell reaches a steady state with the temperature at each point within it remaining constant in time. (a) Explain why the rate of energy transfer P must be the same through each spherical surface, of radius r, within the shell and must satisfy dT_ dr 4rkr? (b) Next, prove that r0.07 r-2 dr 4 Tk Joos 40 dT = where Tis in degrees Celsius and ris in meters. (c) Find the rate of energy transfer through the shell. (d) Prove that dT = 1.84 Jo.03 | r? dr where Tis in degrees Celsius and r is in meters. (e) Find the temperature within the shell as a function of radius. (f) Find the temperature at r = 5.00 cm, halfway through the shell.

Chapter 19 Solutions

Physics for Scientists and Engineers

Ch. 19 - If water with a mass mk at temperature Tk is...Ch. 19 - An aluminum calorimeter with a mass of 100 g...Ch. 19 - An electric drill with a steel drill bit of mass m...Ch. 19 - A 3.00-g copper coin at 25.0C drops 50.0 m to the...Ch. 19 - How much energy is required to change a 40.0-g ice...Ch. 19 - Prob. 11PCh. 19 - A 3.00-g lead bullet at 30.0C is fired at a speed...Ch. 19 - In an insulated vessel, 250 g of ice at 0C is...Ch. 19 - Prob. 14PCh. 19 - One mole of an ideal gas is warmed slowly so that...Ch. 19 - (a) Determine the work done on a gas that expands...Ch. 19 - A thermodynamic system undergoes a process in...Ch. 19 - Why is the following situation impossible? An...Ch. 19 - A 2.00-mol sample of helium gas initially at 300...Ch. 19 - (a) How much work is done on the steam when 1.00...Ch. 19 - A 1.00-kg block of aluminum is warmed at...Ch. 19 - In Figure P19.22, the change in internal energy of...Ch. 19 - A student is trying to decide what to wear. His...Ch. 19 - A concrete slab is 12.0 cm thick and has an area...Ch. 19 - Two lightbulbs have cylindrical filaments much...Ch. 19 - Prob. 26PCh. 19 - (a) Calculate the R-value of a thermal window made...Ch. 19 - Prob. 28PCh. 19 - Gas in a container is at a pressure of 1.50 atm...Ch. 19 - Prob. 30APCh. 19 - You have a particular interest in automobile...Ch. 19 - You are working in a condensed-matter laboratory...Ch. 19 - Prob. 33APCh. 19 - Prob. 34APCh. 19 - Prob. 35APCh. 19 - Prob. 36APCh. 19 - An ice-cube tray is filled with 75.0 g of water....Ch. 19 - Prob. 38APCh. 19 - An iron plate is held against an iron wheel so...Ch. 19 - One mole of an ideal gas is contained in a...Ch. 19 - Prob. 41APCh. 19 - Prob. 42APCh. 19 - Prob. 43APCh. 19 - A student measures the following data in a...Ch. 19 - (a) The inside of a hollow cylinder is maintained...Ch. 19 - A spherical shell has inner radius 3.00 cm and...Ch. 19 - Prob. 47CP
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