Chapter 4: Problem 121
What are the environmental factors that affect the growth rate of microorganisms in foods?
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Chapter 4: Problem 121
What are the environmental factors that affect the growth rate of microorganisms in foods?
These are the key concepts you need to understand to accurately answer the question.
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The thermal conductivity of a solid whose density and specific heat are known can be determined from the relation \(k=\alpha / \rho c_{p}\) after evaluating the thermal diffusivity \(\alpha\). Consider a 2-cm-diameter cylindrical rod made of a sample material whose density and specific heat are \(3700 \mathrm{~kg} / \mathrm{m}^{3}\) and \(920 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), respectively. The sample is initially at a uniform temperature of \(25^{\circ} \mathrm{C}\). In order to measure the temperatures of the sample at its surface and its center, a thermocouple is inserted to the center of the sample along the centerline, and another thermocouple is welded into a small hole drilled on the surface. The sample is dropped into boiling water at \(100^{\circ} \mathrm{C}\). After \(3 \mathrm{~min}\), the surface and the center temperatures are recorded to be \(93^{\circ} \mathrm{C}\) and \(75^{\circ} \mathrm{C}\), respectively. Determine the thermal diffusivity and the thermal conductivity of the material.
In what medium is the lumped system analysis more likely to be applicable: in water or in air? Why?
An electronic device dissipating \(20 \mathrm{~W}\) has a mass of \(20 \mathrm{~g}\), a specific heat of \(850 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), and a surface area of \(4 \mathrm{~cm}^{2}\). The device is lightly used, and it is on for \(5 \mathrm{~min}\) and then off for several hours, during which it cools to the ambient temperature of \(25^{\circ} \mathrm{C}\). Taking the heat transfer coefficient to be \(12 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the temperature of the device at the end of the 5 -min operating period. What would your answer be if the device were attached to an aluminum heat sink having a mass of \(200 \mathrm{~g}\) and a surface area of \(80 \mathrm{~cm}^{2}\) ? Assume the device and the heat sink to be nearly isothermal.
An 18-cm-long, 16-cm-wide, and 12 -cm-high hot iron block \(\left(\rho=7870 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=447 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) initially at \(20^{\circ} \mathrm{C}\) is placed in an oven for heat treatment. The heat transfer coefficient on the surface of the block is \(100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If it is required that the temperature of the block rises to \(750^{\circ} \mathrm{C}\) in a 25 -min period, the oven must be maintained at (a) \(750^{\circ} \mathrm{C}\) (b) \(830^{\circ} \mathrm{C}\) (c) \(875^{\circ} \mathrm{C}\) (d) \(910^{\circ} \mathrm{C}\) (e) \(1000^{\circ} \mathrm{C}\)
A 5-cm-high rectangular ice block \((k=2.22 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(\left.\alpha=0.124 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\right)\) initially at \(-20^{\circ} \mathrm{C}\) is placed on a table on its square base \(4 \mathrm{~cm} \times 4 \mathrm{~cm}\) in size in a room at \(18^{\circ} \mathrm{C}\). The heat transfer coefficient on the exposed surfaces of the ice block is \(12 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Disregarding any heat transfer from the base to the table, determine how long it will be before the ice block starts melting. Where on the ice block will the first liquid droplets appear?
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