Chapter 4: Problem 127
What is the effect of cooking on the microorganisms in foods? Why is it important that the internal temperature of a roast in an oven be raised above \(70^{\circ} \mathrm{C}\) ?
Chapter 4: Problem 127
What is the effect of cooking on the microorganisms in foods? Why is it important that the internal temperature of a roast in an oven be raised above \(70^{\circ} \mathrm{C}\) ?
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Get started for freeA 40 -cm-thick brick wall \((k=0.72 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and \(\alpha=1.6 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\) ) is heated to an average temperature of \(18^{\circ} \mathrm{C}\) by the heating system and the solar radiation incident on it during the day. During the night, the outer surface of the wall is exposed to cold air at \(-3^{\circ} \mathrm{C}\) with an average heat transfer coefficient of $20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\(. Determine the wall temperatures at distances 15,30 , and \)40 \mathrm{~cm}\( from the outer surface for a period of \)2 \mathrm{~h}$.
A long 35-cm-diameter cylindrical shaft made of stainless steel $304\left(k=14.9 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \rho=7900 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=477 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right.\(, and \)\alpha=3.95 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\( ) comes out of an oven at a uniform temperature of \)500^{\circ} \mathrm{C}$. The shaft is then allowed to cool slowly in a chamber at \(150^{\circ} \mathrm{C}\) with an average convection heat transfer coefficient of \(h=60 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Solve this problem using the analytical one-term approximation method. Answers: \(486^{\circ} \mathrm{C}, 22,270 \mathrm{~kJ}\)
Consider a 7.6-cm-diameter cylindrical lamb meat chunk $\left(\rho=1030 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=3.49 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, k=0.456 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right.$, \(\alpha=1.3 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) ). Such a meat chunk intially at \(2^{\circ} \mathrm{C}\) is dropped into boiling water at \(95^{\circ} \mathrm{C}\) with a heat transfer coefficient of $1200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. The time it takes for the center temperature of the meat chunk to rise to \(75^{\circ} \mathrm{C}\) is (a) \(136 \mathrm{~min}\) (b) \(21.2 \mathrm{~min}\) (c) \(13.6 \mathrm{~min}\) (d) \(11.0 \mathrm{~min}\) (e) \(8.5 \mathrm{~min}\)
In areas where the air temperature remains below \(0^{\circ} \mathrm{C}\) for prolonged periods of time, the freezing of water in underground pipes is a major concern. Fortunately, the soil remains relatively warm during those periods, and it takes weeks for the subfreezing temperatures to reach the water mains in the ground. Thus, the soil effectively serves as an insulation to protect the water from the freezing atmospheric temperatures in winter. The ground at a particular location is covered with snowpack at $-8^{\circ} \mathrm{C}$ for a continuous period of 60 days, and the average soil properties at that location are $k=0.35 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\( and \)\alpha=0.15 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}$. Assuming an initial uniform temperature of \(8^{\circ} \mathrm{C}\) for the ground, determine the minimum burial depth to prevent the water pipes from freezing.
Citrus trees are very susceptible to cold weather, and extended exposure to subfreezing temperatures can destroy the crop. In order to protect the trees from occasional cold fronts with subfreezing temperatures, tree growers in Florida usually install water sprinklers on the trees. When the temperature drops below a certain level, the sprinklers spray water on the trees and their fruits to protect them against the damage the subfreezing temperatures can cause. Explain the basic mechanism behind this protection measure, and write an essay on how the system works in practice.
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