1) Geothermal Heat Pump: The equilibrium temperature a few meters below the ground is fairly constant and is warmer than winter surface temperatures and cooler than summer surface temperatures. In many (most) cases, this is a great way to save energy. We're going to explore some of its limitations. a) The temperature underground in Las Vegas (once you are deep enough) is roughly 15 C. The specific heat capacity of sandstone is roughly 1000 J/kg K and the mass density of sandstone is 2000 kg/m³. Suppose your reservoir is a 10x10x10 meter cubical volume of sandstone under your house and that the average equilibrium temperature in your home would be 40 C (104 F) during the summer. The mass of a home, and all of the furnishings, weighs roughly 250,000 kg and has a specific heat capacity of 1200 J/kg K. If left isolated from the environment, what is the final equilibrium temperature of the home/heat reservoir system? b) With the sun shining, the home absorbs an average of 15,000 Watts. Beginning at its initial temperature of 15 C, and assuming that the energy is quickly absorbed by the sandstone reservoir, how long will it take before the reservoir is in equilibrium with the outdoor temperature of 40 C? What is this time in days?
1) Geothermal Heat Pump: The equilibrium temperature a few meters below the ground is fairly constant and is warmer than winter surface temperatures and cooler than summer surface temperatures. In many (most) cases, this is a great way to save energy. We're going to explore some of its limitations. a) The temperature underground in Las Vegas (once you are deep enough) is roughly 15 C. The specific heat capacity of sandstone is roughly 1000 J/kg K and the mass density of sandstone is 2000 kg/m³. Suppose your reservoir is a 10x10x10 meter cubical volume of sandstone under your house and that the average equilibrium temperature in your home would be 40 C (104 F) during the summer. The mass of a home, and all of the furnishings, weighs roughly 250,000 kg and has a specific heat capacity of 1200 J/kg K. If left isolated from the environment, what is the final equilibrium temperature of the home/heat reservoir system? b) With the sun shining, the home absorbs an average of 15,000 Watts. Beginning at its initial temperature of 15 C, and assuming that the energy is quickly absorbed by the sandstone reservoir, how long will it take before the reservoir is in equilibrium with the outdoor temperature of 40 C? What is this time in days?
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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Transcribed Image Text:**1) Geothermal Heat Pump:** The equilibrium temperature a few meters below the ground is fairly constant and is warmer than winter surface temperatures and cooler than summer surface temperatures. In many (most) cases, this is a great way to save energy. We’re going to explore some of its limitations.
a) The temperature underground in Las Vegas (once you are deep enough) is roughly 15°C. The specific heat capacity of sandstone is roughly 1000 J/kg·K and the mass density of sandstone is 2000 kg/m³. Suppose your reservoir is a 10x10x10 meter cubical volume of sandstone under your house and that the average equilibrium temperature in your home would be 40°C (104°F) during the summer. The mass of a home, and all of the furnishings, weighs roughly 250,000 kg and has a specific heat capacity of 1200 J/kg·K. If left isolated from the environment, what is the final equilibrium temperature of the home/heat reservoir system?
b) With the sun shining, the home absorbs an average of 15,000 Watts. Beginning at its initial temperature of 15°C, and assuming that the energy is quickly absorbed by the sandstone reservoir, how long will it take before the reservoir is in equilibrium with the outdoor temperature of 40°C? What is this time in days?
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