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A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with Vo (ft') of warm milk at a temperature of To (°F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at To (°F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to VT after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.

A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with Vo (ft') of warm milk at a temperature of To (°F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at To (°F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to VT after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with Vo (ft') of warm milk at a temperature of To (°F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at To (°F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to VT after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.
Transcribed Image Text:A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with Vo (ft') of warm milk at a temperature of To (°F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at To (°F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to VT after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.
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