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It is a hot day in Atlanta and you and your friends bought an ice cream maker. The unit consists of a bowl and a base that rotates the bowl around a stationary mixing paddle. The walls of the bowl contain an unknown mixture thatabsorbs heat from the ice cream. The bowl must be frozen -20°C) before use. Unfortunately, your friends have lost the instructions and can't remember how long to operate the unit. You tell them not to worry since you have mastered energy conservation problems and can calculate the amount of time required to freeze the ice cream. Looking at the box, you find the specifications for the unit: a) Inner surface area of freezing bowl: 600 cm2; b) Heat transfer coefficient for bowl:h = 0.025 J / (cm2 s °C); c) Power required to stir the bowl (100% efficiency): 25 W; d) Amount of ice cream mixture added: 1 kg, e) The rate of heat transfer is between the bowl and the milk. You know that solutes lower the freezing point of water. Assume that the freezing point is lowered to 5'C, The main component of the ice cream mixture is milk and also cream, sugar, and vanilla extract. To achieve the consistency of soft-serve ice cream, only half of the water must be kJ frozen. At 5°C, AĦfwater 300 /kg Derive an equation, in terms of the above variables, and estimate the total operating time.

It is a hot day in Atlanta and you and your friends bought an ice cream maker. The unit consists of a bowl and a base that rotates the bowl around a stationary mixing paddle. The walls of the bowl contain an unknown mixture thatabsorbs heat from the ice cream. The bowl must be frozen -20°C) before use. Unfortunately, your friends have lost the instructions and can't remember how long to operate the unit. You tell them not to worry since you have mastered energy conservation problems and can calculate the amount of time required to freeze the ice cream. Looking at the box, you find the specifications for the unit: a) Inner surface area of freezing bowl: 600 cm2; b) Heat transfer coefficient for bowl:h = 0.025 J / (cm2 s °C); c) Power required to stir the bowl (100% efficiency): 25 W; d) Amount of ice cream mixture added: 1 kg, e) The rate of heat transfer is between the bowl and the milk. You know that solutes lower the freezing point of water. Assume that the freezing point is lowered to 5'C, The main component of the ice cream mixture is milk and also cream, sugar, and vanilla extract. To achieve the consistency of soft-serve ice cream, only half of the water must be kJ frozen. At 5°C, AĦfwater 300 /kg Derive an equation, in terms of the above variables, and estimate the total operating time.

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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**Understanding the Ice Cream Maker Operation** On a hot day in Atlanta, you and your friends decided to make ice cream using an ice cream maker. This educational guide explains the process and calculations involved in using the maker to ensure efficient operation. ### Components of the Ice Cream Maker - **Unit Description**: Consists of a bowl and a stationary mixing paddle. The bowl must be frozen before use to facilitate the ice cream-making process. ### Key Specifications and Inputs 1. **Bowl Information**: - Temperature to which the bowl should be lowered: **-20°C** - Inner surface area of the freezing bowl: **600 cm²** 2. **Heat Transfer**: - Heat transfer coefficient for the bowl (assuming 100% efficiency): **25 W** - Heat transfer rate between the bowl and the mixture (Q): **0.0025 J/cm²·s·°C** 3. **Ice Cream Mixture Details**: - Amount of mixture added: **1 kg** - Main components: Milk, sugar, vanilla extract 4. **Freezing Requirements**: - Temperature the ice cream mixture needs to be lowered to: **5°C** - Heat of fusion (energy required to freeze) of water: **300 J/g** ### Energy Considerations - To freeze the ice cream, you must calculate the energy needed. This involves understanding that the mixture's freezing point is slightly lower due to solutes. - For soft-serve ice cream, only half of the water content needs to be frozen. ### Calculations 1. **Determine Energy Required**: - Use the formula for energy change considering the heat transfer rate and surface area. 2. **Calculate Time**: - Estimate the total operating time by dividing the required energy by the product of transfer rate and the area. ### Conclusion Through a careful calculation of energies and understanding the heat dynamics, you can accurately estimate the time required to make ice cream using your ice cream maker. This ensures the mixture reaches the desired consistency and temperature efficiently, making your dessert preparation process a success.
Transcribed Image Text:**Understanding the Ice Cream Maker Operation** On a hot day in Atlanta, you and your friends decided to make ice cream using an ice cream maker. This educational guide explains the process and calculations involved in using the maker to ensure efficient operation. ### Components of the Ice Cream Maker - **Unit Description**: Consists of a bowl and a stationary mixing paddle. The bowl must be frozen before use to facilitate the ice cream-making process. ### Key Specifications and Inputs 1. **Bowl Information**: - Temperature to which the bowl should be lowered: **-20°C** - Inner surface area of the freezing bowl: **600 cm²** 2. **Heat Transfer**: - Heat transfer coefficient for the bowl (assuming 100% efficiency): **25 W** - Heat transfer rate between the bowl and the mixture (Q): **0.0025 J/cm²·s·°C** 3. **Ice Cream Mixture Details**: - Amount of mixture added: **1 kg** - Main components: Milk, sugar, vanilla extract 4. **Freezing Requirements**: - Temperature the ice cream mixture needs to be lowered to: **5°C** - Heat of fusion (energy required to freeze) of water: **300 J/g** ### Energy Considerations - To freeze the ice cream, you must calculate the energy needed. This involves understanding that the mixture's freezing point is slightly lower due to solutes. - For soft-serve ice cream, only half of the water content needs to be frozen. ### Calculations 1. **Determine Energy Required**: - Use the formula for energy change considering the heat transfer rate and surface area. 2. **Calculate Time**: - Estimate the total operating time by dividing the required energy by the product of transfer rate and the area. ### Conclusion Through a careful calculation of energies and understanding the heat dynamics, you can accurately estimate the time required to make ice cream using your ice cream maker. This ensures the mixture reaches the desired consistency and temperature efficiently, making your dessert preparation process a success.
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