ENERGY AND ENVIRONMENT I CLASS DATA

Energy & Environment I

HW#2 with a solution

Due Friday, Oct 12, 2001

Residential costs of energy. Determine the typical costs of the following energies for our region:

Electricity: my electric bill for September 2001 shows the following rates:

6-10 AM and 5-9 PM charge: 7.91 cents/kwh
10 AM to 5 PM charge: 7.02 cents/kwh
9 PM to 6 AM, Sunday, and Holiday charge: 6.36 cents/kwh
Total charge with customer charge, conservation credits and charges, and city tax: 5.78 cents/kwh

Natural Gas: my natural gas bill for September 2001 shows the following rates:

Cost the gas prior to 9/1/01: 70.64 cents/therm
Cost of gas from 9/1/01 on: 62.95 cents/therm
Distribution charge: 22.49 cents/therm
Total charge with customer charge, conservation charge, and city tax: $1.28/therm

For comparison, the total charge for February 2001 (when the cost of gas was 70.64 cents/therm and when much more gas was used): $1.00/therm. (The nonlinearity of cost with amount used is caused by the customer charge, which does do decrease in proportion to smaller amounts used.)

Gasoline: when I filled up with 89 octane gasoline last weekend, the cost was $1.79 per gallon.

Rank-order these by the cost per unit of energy purchased. Convert to a common unit of energy (kJ = kilojoule). This is done as follows:

Electricity: 1 kwh = 3600 kJ. Thus, my cost of electricity is (0.0578 $/kwh)/(3600 kJ/kwh) = 1.606 x 10^-5 $/kJ.

Natural gas: Let’s use my $1.00/therm charge, since this is representative of the heating season when significant amounts of gas are used. Let’s decrease this by the price drop of natural gas on 9/1/01: 7.69 cents/therm. Thus, our adjusted cost is 0.9231 $/therm. There are 100,000 BTUs in a therm and 1.055 kJ in a BTU. One therm has 105,500 kJ. Thus, my cost for the coming season could be: (0.9231 $/therm)/(105,500 kJ/therm) = 8.750 x 10^-6 $/kJ. (Note: the current spot price for natural gas is about 20 cents per therm. Thus, my cost over the upcoming heating season may drop further.)
Gasoline: Bodansky, on page 3:5 of the Course Notes, tells us the heating value of gasoline is 5.253 x 10⁶ BTUs per barrel, which is equal to 5.542 x 10⁶ kJ/barrel. A standard barrel contains 42 US gallons. The heating value can be expressed as 131,950 kJ/gallon. Thus, the cost of my gasoline is: (1.79 $/gallon)/ (131,950 kJ/gallon) = 1.357 x 10^-5 $/kJ.

The order in cost per energy unit, as $/kJ, from low to high, with electricity as 1, is as follows:

0.545: natural gas

0.845: gasoline

1.000: electricity

For one year, plot the energy consumption of your residence, or that of your family residence. Plot the following versus month, use one graph for all three plots:

Electricity as kwh/day vs month. See spread sheet and graph below.
Natural gas or propane (if used) as kwh/day vs month. See spread sheet and graph below.
Total energy as kwh/day vs month. See spread sheet and graph below.

If you do not have the data for your residence use the data for the residence below.

Then determine the energy costs (as $) for the year. Determine the electricity cost, the natural gas or propane cost (if used), and the total cost. See spread sheet below.

Explain, justify: Which is cheaper to use for heating: electricity or natural gas? Note: electric furnaces and base board heaters are about 100% efficient, natural gas furnaces are about 80% efficient, and electric heat pumps are about 200% efficient. This is done as follows:

Electric furnace or baseboard heater: we are assuming all of energy purchased goes into space heating. This is nearly the case, though it takes some electricity to run the air blower of the forced-air electric furnace. Thus, the cost is 5.78 cents per kwh of heat delivered.
Natural gas furnace: we assume 80% of the energy purchased goes into space heating. Note: this is the minimum efficiency of gas furnaces sold today. Let’s use the price of 8.750 x 10^-6 $/kJ. Multiplying by 3600 kJ/kwh and dividing by 0.80 gives our heating cost of 3.94 cents per kwh of heat delivered.
Electric heat pump: the coefficient of performance for electric heat pumps operated in Western Washington is about 2.0. This translates into an effective efficiency of 200%. Thus, the cost of heating with the electric heat pump is one-half that of the electric furnace and baseboard heater: 2.89 cents per kwh of heat delivered.
Thus, given the current costs of electricity and natural gas, the rank order from low to high, with the electric furnace/baseboard heater being 1.0 is as follows:

0.500: electric heat pump

0.682: natural gas furnace

1.000: electric furnace and baseboard heater

Electricity and Natural Gas Use and Costs for Residence in Western Washington.

Electricity used for lighting and appliances.

Natural gas used for space heating and water heating.

Date	Month	Electric	Natural Gas	Natural Gas	Total Energy	Electric	Electric	NG	NG	Total Energy
on Bill	of Bill	Ave kwh/day	Ave therm/day	Ave kwh/day	Ave kwh/day	Ave $/day	$/month	Ave $/day	$/month	Ave $/day
8/17/2000	1	28	0.3	8.8	36.8	$1.62	$50.17	$0.28	$8.58	$1.90
9/17/2000	2	32	0.4	11.7	43.7	$1.85	$55.49	$0.37	$11.08	$2.22
10/17/2000	3	37	1.5	44.0	81.0	$2.14	$66.30	$1.38	$42.92	$3.52
11/17/2001	4	37	4.3	126.0	163.0	$2.14	$64.16	$3.97	$119.08	$6.11
12/17/2000	5	37	6.5	190.5	227.5	$2.14	$66.30	$6.00	$186.00	$8.14
1/17/2001	6	27	5.6	164.1	191.1	$1.56	$48.38	$5.17	$160.25	$6.73
2/17/2001	7	26	5.9	172.9	198.9	$1.50	$42.08	$5.45	$152.50	$6.95
3/17/2001	8	27	4.9	143.6	170.6	$1.56	$48.38	$4.52	$140.22	$6.08
4/17/2001	9	33	4.2	123.1	156.1	$1.91	$57.22	$3.88	$116.31	$5.78
5/17/2001	10	32	2.0	58.6	90.6	$1.85	$57.34	$1.85	$57.23	$3.70
6/17/2001	11	29	0.9	26.4	55.4	$1.68	$50.29	$0.83	$24.92	$2.51
7/17/2001	12	26	0.4	11.7	37.7	$1.50	$46.59	$0.37	$11.45	$1.87
Total						Note 1	$652.68	Note 2	$1,030.55	$1683
Note 1	Assuming a constant cost of 5.78 cents per kwh						Electric		NG cost	Total energy
Note 2	Assuming a constant cost of 92.31 cents per therm. This under-predicts the summertime costs. cost for year								for year	cost for year