(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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Chapter 20 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m K and 0.020 W/m K, respectively, while other tissues inside the body have conductivities of about 0.50 W/m K. Assume that between the core region of the body and the skin sin face lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues. (a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits. (b) Find the rate of energy loss when the core temperature is 37C and the exterior temperature is 0C. Assume that both a protective layer of clothing and an insulating layer of unmoving air a absent, and a body area of 2.0 m2.arrow_forwardAn 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 hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0C. It is completely filled with turpentine at 20.0C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0C. (a) How much turpentine overflows? (b) What is the volume of the turpentine remaining in the cylinder at 80.0C? (c) If the combination with this amount of turpentine is then cooled back to 20.0C, how far below the cylinders rim does the turpentines surface recede?arrow_forward
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- When builders were constructing a sidewalk they forgot to include an expansion joint between two of the segments, L = 2.1 m at To = 20° C. Assume the opposite ends of each segment are fixed and the linear expansion coefficient is α = 11 × 10-6 °C-1. a.) As the day heats to Tb the segments press against each other and begin to raise the junction a distance h forming a triangle. What is the height (in meters) at Tb=110° F? b.) What should the gap have been, in units of meters, to prevent them from touching?arrow_forwardA walrus transfers energy by conduction through its blubber at the rate of 150 W when immersed in −1.00ºC water. The walrus’s internal core temperature is 37.0ºC , and it has a surface area of 2.00 m2 . What is the average thickness of its blubber, which has the conductivity of fatty tissues without blood?arrow_forwardAn isolated bar is kept at zero temperature at its ends. If it's given initially temperature, f(x) = 100°C, a2y equation u (x, t) is equal to: a2y so the bar temperature ax2 %3D u (0, t) u (L, t) [sin#x•e) , sin x -400 -400 (sinx-e ) + TC .x. (25x² sinx e sin x-e ) The Answer Is the Answer is O Isinx e e sin 400 None of all 3. 25m sin x earrow_forward
- You drop a 7 mole piece of zinc, which has been heated to 423 K into 0.101 kg of water at 300 K You can use equipartition for the zinc. Assume that the system (water+zinc) is completely isolated from the environment. The specific heat capacity of water is 4.186 J/g K. What is the change in temperature of the water? (a) 16.9 K (b) 175. K (c) 36.0 K (d) 50.8 K (e) 6.85 K ✔100% Did the entropy of the zinc increase, decrease or stay the same? (a) Increase (b) Decrease) (0) Stay the samearrow_forwardI.C 02/A/ Use the Crank-Nicolson method to solve for the temperature distribution of a long thin rod with a length of 10 cm and the following values: k = 0.49 cal/(s cm °C), Ax = 2 cm, and At = st 0.1 s. Initially the temperature of the rod is 0°C and the boundary conditions are fixed for all times at 7(0, t) = 100°C and 7(10, t) = 50°C. Note that the rod is aluminum with C = 0.2174 cal/g °C) and p = 2.7 g/cm³. List the tridiagonal system of equations and determined the temperature up to 0.1 s.arrow_forwardFollowing a collision in outer space, a copper disk at 850°C is rotating about its axis with an angular speed of 25.0 rad/s. As the disk radiates infrared light, its temperature falls to 20.0°C. No external torque acts on the disk. (a) Does the angular speed change as the disk cools? Explain how it changes or why it does not. (b) What is its angular speed at the lower temperature?arrow_forward
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