Me 4530 Alternative Energy Systems Assessment Answers

Questions:

Answer:

We know that, 1 BTU = 0.293 Wh.

1000 BTU = 0.293 KWh.

Now, cost of 1 KWh = $0.12.

Hence, cost of 0.293 KWh = $0.04.

Now, the money that can be saved in months from November-April each year is calculated in excel given below.

Hence, it will take 5 years that is from 2005 to 2010 to pay back the total investment.

Response to question 2:

The three types of windows that have U factor more than the current window U factor of 0.81 Btu/ are given below.

Type A window U factor = 0.85 Btu/.

Type B window U factor = 0.92 Btu/.

Type C window U factor = 1.02 Btu/.

Now, putting the values of U factor in the excel we automatically get the small table of UgAg, UbAb, UaAa and inflit. The UoAo value is the sum of all the above-mentioned U factors.

The formulas of calculating the different values of UgAg, UbAb, UaAa and inflit with respect to different U factors are given in the excel file.

Table for current U factor of 0.81 Btu/:

Table for U factor of 0.85 Btu/:

Now, only the window UwAw will change due to the U factor change and area change.

Now, putting the values of U factor in the excel we automatically get the small table of UgAg, UbAb, UaAa and inflit. The UoAo value is the sum of all the above-mentioned U factors.

The formulas of calculating the different values of UgAg, UbAb, UaAa and inflit with respect to different U factors are given in the excel file.

Table for current U factor of 0.81 Btu/:

Table for U factor of 0.85 Btu/:

Now, only the window UwAw will change due to the U factor change and area change.

Area of window = 5ft*3ft = 15 ft^2.

So, UwAw = 0.85*15 = 12.75 Btu/

Table for U factor of 0.92 Btu/:

Now, the area of window remains the same = 15 ft^2.

So, UwAw = 0.92*15 = 13.8 Btu/

Table for U factor of 1.02 Btu/:

Here, UwAw = 1.02*15 = 15.3 Btu/

Given that the cost of each storm window is $75.

Hence, the cost of 3 storm windows = 3*75 = $225

Now, the U factor of a typical storm window is 0.45 Btu/.

Now, area of the window is assumed to be Aw = 32*22 ft^2 = 704 ft^2.

Hence, UwAw = 0.45*704 = 316.8 Btu/.

Now, total wall area as obtained from the question is 4110 ft^2.

Now, the % of window = 704/4110 = 17.13%.

Now, Ag = 4110*17.13/100 = 704.043 ft^2.

Hence, UgAg = 0.45*704.043 = 316.82.

Response to question 4:

Now, the cost of XPS installation for insulation of 1000 ft^2 is $2,361.37.

Cost of drywall installation is $1.50 per square feet.

Now, the total wall area = 4110 ft^2.

Now, the window area Aw = 3370.2 ft^2.

Ag = 739.8 ft^2.

Hence, the cost of XPS installation = (2361.37/1000) *4000 = $9445.48.

Now, the cost of drywall installation = 1.50*4110 = $6165.

Hence, the cost increased by XPS installation = $9445.48 - $6165 = $3280.48.

Now, assuming the cost saved in each year as obtained from question 1 is the average of the cost saved in 7 years = $230.45.

Now, the time that will be taken for payback = $3280.48/$230.45 ~ 15 years.

Now, after getting 50% discount on the XPS the cost becomes $9445.48*0.5 = $4722.74

Now, as the 4 layers of 2-inch thick XPS coating is put in the wall hence the total cost o XPS insulation becomes $4722.74*4 = $18890.96.

Now, as the net area increases the values of UgAg and UwAw also increases.

Now, the advantages of XPS insulation over fibreglass insulation are

1) XPS is a solid material and it remains solid under any atmospheric condition and hence resists the air flow. Whereas, the fibreglass has many cavities and air flows through those cavities into house.

2) Fibreglass allows insects to live inside it in bad weather condition and hence insects can enter in the house but due to the hard and cold backside of the XPS coating insects cannot enter through it.

3) XPS is nearly moisture-proof but through fibreglass moisture can enter in the house.

The total cost R-13 fibreglass insulation including material, Labour and supplies and tools is $1,193.57 for 1000 square feet.

Now, the area of the basement = 2704.94 ft^2.

Now, the costing of the R-13 fibreglass insulation in basement area = 2704.94*$1,193.57/1000 = $3228.535.

Hence, the payback period of the improvement assuming the average saving in a year is $230.45 will be = $3228.535/$230.45 ~ 14 years.

Response to question 7:

The area of the attic was previously 2704.94 ft^2.

Now, after adding an additional 3.5 inches onto the existing attic insulation the area changes by 3.5^2 = 12.25 ft^2.

Now, the area of attic becomes Aa = 2704.94 + 12.25 = $2717.19.

Now, the U factor of the material installed on the attic if known will be multiplied by the area Aa to get the value of UaAa.

Response to question 8:

RESNET document in Moodle on air infiltration is needed to answer this question.

Response to question 9:

The current value of UoAo is 995.86 Btu/hr°F.

Now, there are two ways to reduce the value of UoAo to its 50% that is 497.93 Btu/hr°F.

The first is to reduce the effective areas of walls, glass, basement and attic so that the overall cost reduces. The second method is to use a different material for the walls, glass, basement and attic so that the U factors are different. Now, as the areas cannot be reduced hence the best method is to use different materials.

Hence, the adjusted U factors of materials used in walls, glass, basement and attic will be,

Uw = 0.038 Btu/

Ug = 0.364 Btu/

Ub = 0.0447 Btu/

Ua = 0.0092 Btu/

Response to question 10:

Now, considering the lowest possible value of U factor from question 8.

Hence, the lowest value of UoAo is calculated below.

Hence, the total BTU consumption from November-April will be = 663.15*24*30*8= 3819750.14 = (3819750.14/1000)*0.293 = 1119.187 KWh.

Now, the costing of 1119.187 KWh = 1119.187*0.12 = $134.3024.

This costing can be payed back inside 1 year and hence reducing the UoAo value reduces the costing.