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Microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When the food is initially frozen, however, the water molecules do not readily oscillate in response to the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be dissipated in the form of heat to prevent damage to the generator.) (a) Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T₁ = -20°C placed in a microwave oven with T = 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power (P = 1kW total) is absorbed in the food. (b) After all the ice is converted to liquid, determine how long, in min, it will take to heat the beef to T, = 80°C if 95% of the oven power is absorbed in the food. Assume the properties of the beef are the same as liquid water.

Microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When the food is initially frozen, however, the water molecules do not readily oscillate in response to the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be dissipated in the form of heat to prevent damage to the generator.) (a) Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T₁ = -20°C placed in a microwave oven with T = 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power (P = 1kW total) is absorbed in the food. (b) After all the ice is converted to liquid, determine how long, in min, it will take to heat the beef to T, = 80°C if 95% of the oven power is absorbed in the food. Assume the properties of the beef are the same as liquid water.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When the food is initially frozen, however, the water molecules do not readily oscillate in response to the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be dissipated in the form of heat to prevent damage to the generator.) (a) Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T₁ = -20°C placed in a microwave oven with To = 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power (P = 1 kW total) is absorbed in the food. (b) After all the ice is converted to liquid, determine how long, in min, it will take to heat the beef to Tf power is absorbed in the food. Assume the properties of the beef are the same as liquid water. Part A To Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T; = -20°C placed in a microwave oven with 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power ( P = 1 kW total) is absorbed in the food. = ta = i = 80°C if 95% of the oven min
Transcribed Image Text:Microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When the food is initially frozen, however, the water molecules do not readily oscillate in response to the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be dissipated in the form of heat to prevent damage to the generator.) (a) Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T₁ = -20°C placed in a microwave oven with To = 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power (P = 1 kW total) is absorbed in the food. (b) After all the ice is converted to liquid, determine how long, in min, it will take to heat the beef to Tf power is absorbed in the food. Assume the properties of the beef are the same as liquid water. Part A To Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T; = -20°C placed in a microwave oven with 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power ( P = 1 kW total) is absorbed in the food. = ta = i = 80°C if 95% of the oven min
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