Mass and Energy Units (Climate Resilient Futures)

Hypothetical Home 

A single-family, detached home has the following characteristics: 

Dimensions (40’x20’10’, as shown in the figure above)

• 6 single-glazed, wood-framed glass windows that are each 2′ x 4′
• The walls, ceiling and door have an R value of 4 (ft2 °F hr)/Btu
• The ceiling has an additional 1-inch polystyrene insulation layer
• The temperature in the home is maintained at 68°F by a natural gas-fueled heater, which runs at
• 80% efficiency

For the problems in this assignment, we’ll work with the following assumptions:

There is no heat loss through the floor/foundation to the ground

• The house is well-sealed and there are no leaks
• The temperature outdoors is a constant 10°F
• Heating costs 

1. If natural gas costs $16.28 per thousand cubic feet, how much would it cost to heat this home over your hypothetical month? 

Weatherization 

2. How much heat would be lost through the windows, ceiling and walls if the home described above was retrofit so that: 

The walls and ceiling now have an R value of 19 (the original 1-inch polystyrene insulationlayer on the ceiling was replaced so the total value for both the walls and ceiling is now 19).

• The windows are replaced with argon-filled, triple-glazed windows with low E coating
• (see Table 4.2 on Page 2 of this assignment).

3. How much natural gas (in cubic feet) would be needed to heat the now-weatherized home

for a month?

4. With a natural gas cost of $16.28 per thousand cubic feet, what would be the cost to heat

the weatherized home for a month?

Heat Pumps

5. Assume that the natural gas heater in the hypothetical home is replaced by an air-source

heat pump with 300% efficiency. With 300% efficiency, the heat pump puts out 3 times as

much heat as it uses in electricity. Using the conversion factor of 3412.14 Btu = 1kwh, How

many kWh of electricity would be needed to heat the unweatherized home (described on

Page 1) over the same month? How much would this cost if electricity is $0.23 per kwh?

6. How many kWh of electricity would be needed to heat the retrofitted, weatherized home

(described in Question 2) over the same month? How much would this cost if electricity is

$0.23 per kwh?