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Your family just bought a very small cabin in Estes Park, CO, and they have asked you to help figure out heating costs for the building, Since your grandparents plan to stay at the cabin often and they like it warm, you decide that you need to be able to achieve 23 "C in the winter. Assuming a minimum heat output of 2 people. 2 lamps, a TV, a computer and a refrigerator, you've figured out that a reasonable estimate for total internal gain rate is 600 W. You calculate that the whole building heat transfer coefficient for the existing cabin is 400 W/K. Note that some questions may have values that are randomly generated and will change on second homework attempts. You will need to revise your mathematics, but the methodology and formulas remain the same.

Your family just bought a very small cabin in Estes Park, CO, and they have asked you to help figure out heating costs for the building, Since your grandparents plan to stay at the cabin often and they like it warm, you decide that you need to be able to achieve 23 "C in the winter. Assuming a minimum heat output of 2 people. 2 lamps, a TV, a computer and a refrigerator, you've figured out that a reasonable estimate for total internal gain rate is 600 W. You calculate that the whole building heat transfer coefficient for the existing cabin is 400 W/K. Note that some questions may have values that are randomly generated and will change on second homework attempts. You will need to revise your mathematics, but the methodology and formulas remain the same.

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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Your family just bought a very small cabin in Estes Park, CO, and they have asked you to help figure out heating costs for the building. Since your grandparents plan to stay at the cabin often and they like it warm, you decide that you need to be able to achieve 23 "C in the winter. Assuming a minimum heat output of 2 people, 2 lamps, a TV, a computer and a refrigerator, you've figured out that a reasonable estimate for total internal gain rate is 600 W. You calculate that the whole building heat transfer coefficient for the existing cabin is 400 W/K. Note that some questions may have values that are randomly generated and will change on second homework attempts. You will need to revise your mathematics, but the methodology and formulas remain the same. Question 1 How much heating power (W) would be necessary to keep the cabin interior at 23 Cif the exterior temperature is -10 C? Question 2 Before the following winter, you have implemented some significant energy efficient measures and reduced the whole building heat transfer coefficient to 200 W/K. Still under the decision to achieve 23 "C inside temperature in the winter, you suggest that a compact gas-fired stove would create a nice ambiance while saving your family money compared to other options, such as electric resistance heaters. You look up the average annual minimum temperature in Estes Park, which is -7 "C (winter design temperature). Determine the size (heating capacity) of the stove you would need to meet the peak heating energy that needs to be supplied to the home. (Note: one sizes the furnace for "worst case" conditions, which means that you ignore the benefits of internal gains.). Provide the answer for the furnace size in watts rounded to the nearest watt. Question 3 Given the internal gains, and the whole building heat transfer coefficient of 200 W/K following renovations, below what outdoor air temperature will the cabin need to be actively heated (the balance point temperature)? Question 4 How much will it cost annually to heat the renovated cabin with the gas stove, assuming the stove is 78% efficient and gas costs $2.00/therm? (1 therm = 105,480 kJ). Assume that the Annual Heating Degree Days for the correct teo is 5290 HDD ("C-day). Don't forget the efficiency of the stove, and check your units carefully - it will help avoid mistakes! Also think carefully about the concept and equation for efficiency before just plugging in numbers - should the energy you pay for be more or less than what goes into heating the house? What makes sense? Round your answer to the nearest dollar.
Transcribed Image Text:Your family just bought a very small cabin in Estes Park, CO, and they have asked you to help figure out heating costs for the building. Since your grandparents plan to stay at the cabin often and they like it warm, you decide that you need to be able to achieve 23 "C in the winter. Assuming a minimum heat output of 2 people, 2 lamps, a TV, a computer and a refrigerator, you've figured out that a reasonable estimate for total internal gain rate is 600 W. You calculate that the whole building heat transfer coefficient for the existing cabin is 400 W/K. Note that some questions may have values that are randomly generated and will change on second homework attempts. You will need to revise your mathematics, but the methodology and formulas remain the same. Question 1 How much heating power (W) would be necessary to keep the cabin interior at 23 Cif the exterior temperature is -10 C? Question 2 Before the following winter, you have implemented some significant energy efficient measures and reduced the whole building heat transfer coefficient to 200 W/K. Still under the decision to achieve 23 "C inside temperature in the winter, you suggest that a compact gas-fired stove would create a nice ambiance while saving your family money compared to other options, such as electric resistance heaters. You look up the average annual minimum temperature in Estes Park, which is -7 "C (winter design temperature). Determine the size (heating capacity) of the stove you would need to meet the peak heating energy that needs to be supplied to the home. (Note: one sizes the furnace for "worst case" conditions, which means that you ignore the benefits of internal gains.). Provide the answer for the furnace size in watts rounded to the nearest watt. Question 3 Given the internal gains, and the whole building heat transfer coefficient of 200 W/K following renovations, below what outdoor air temperature will the cabin need to be actively heated (the balance point temperature)? Question 4 How much will it cost annually to heat the renovated cabin with the gas stove, assuming the stove is 78% efficient and gas costs $2.00/therm? (1 therm = 105,480 kJ). Assume that the Annual Heating Degree Days for the correct teo is 5290 HDD ("C-day). Don't forget the efficiency of the stove, and check your units carefully - it will help avoid mistakes! Also think carefully about the concept and equation for efficiency before just plugging in numbers - should the energy you pay for be more or less than what goes into heating the house? What makes sense? Round your answer to the nearest dollar.
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