Question

An individual is building a home in a rural area outside of Lafayette, IN. Natural gas is not available so the individual is considering some different options for heating and cooling the house that are described below. The total heating requirement for the year is estimated to be 150 MMBtu, whereas the total cooling requirement is about 50 MMBtu. The system will be financed along with the rest of the house with a 20% down payment and a loan for 15 years at an interest rate of 3.5%. Assuming a discount rate of 10%, then use the P1‐P2 method to determine the lifecycle costs for each of the different options over the period of the loan. Using the system having the lowest initial cost as a baseline, evaluate the life‐cycle savings and true (not simple) payback periods for the alternatives. Use local energy costs for electricity and liquid propane and report the values and source for the estimates. Assume that the annual inflation rate for electricity is 3% whereas liquid propane inflates at 6% per year. The effective income tax rate for the homeowner including state and federal taxes is 40%. Neglect any differences in maintenance or impacts on property taxes. Make a recommendation regarding the best choice and provide an appropriate justification.

a. Electric Furnace and Conventional Air Conditioner: 1) total installed cost of $3000, 2) electric furnace efficiency of 99%, 3) average COP for cooling of 4.

b. LP (liquid‐propane) Furnace and Conventional Air Conditioner: 1) total installed cost of $4500, 2) average furnace efficiency of 90%, 3) average COP for cooling of 4.

c. Air‐Source Heat Pump: 1) total installed cost of $5500, 2) average COP for cooling of 4, 3) average COP for heating of 2.5.

d. Ground‐Water (Geothermal) Heat Pump: 1) total installed cost of $15,000, 2) average COP for cooling of 6, 3) average COP for heating of 3.5, 4) tax rebate from the federal government of 30% of the installed cost.

Answer 1

Problem 2:

Given,

Indoor conditions:

DBT = 72 ° F & 40 % RH

From psyhrometric it is found that

Dew point temperature corresponding to above conditions is 57.2 °F & hence, this is the dry bulb temperature at which condensation will begin to occur on the surface. This means that inner surface of the window should always be maintained above 57.2 ° F in order avoid any condensation on it. Hence, for 50° F conditions in cold weather, definitely condensation will be happening on the surface.

Problem 3:

Residence space volume = 2000 ft^2 * 8 ft = 16000ft^3

Inside air temperature = 70 °F

Outside ambient temperature = 10 °F

Heat capacity of air = 0.018 Btu per ° F per ft^3

Hence, heat absorbed by ambient air when it fills the room,

= (0.018 Btu per ° F per ft^3 ) * (16000ft^3) * (70 °F - 10 °F)

= 17280 Btu

When this heat is removed in 1 hr,

Rate of heat removal = 17280 Btu per hr