Household Power / Solar Power

Here's the connection to climate change:

  • Global warming is caused by human activities that generate $CO_2$ and other greenhouse gases.
  • Our $CO_2$ emissions are related to
    • the machines we use to generate electricity (25%)
    • Growing, processing, and distributing food (24%)
    • how we make stuff (industry) (21%)
    • the machines we use to get around and transport our stuff (cars and trucks) (about 14%)
  • Our electrical energy is generated, ~65% by burning coal: 60% fossil fuels (19.3% coal and 40.3% natural gas), which generate carbon-dioxide.
  • Transportation is all fossil-fueled, except for biofuels (5%) and electricity & other 2%
  • The amount of carbon-dioxide emitted is directly proportional to the amount of energy we use. [Double the energy use means double the carbon emissions.]

Some orienting questions

  • What household appliances use a lot of / not very much energy?
  • Is the appliance that takes the most power always the one that uses the most energy?
  • What can I do / what can be done to conserve energy?
  • How many solar panels (or how big an area) would be needed to cover my electric usage?

Power at home

...well, actually energy and power

Energy is the potential to change the environment.

Typical units: Calorie, calorie, Joules, BTU, kWh, BOE (Barrels of Oil Equivalent)...

Power is the rate of energy use: Energy divided by time. $$P=E/t$$
Typical units: watts (J/sec), HP (horsepower), ...

1,000 Watts = 1 kiloWatt (kW) = 1,000 J / s

Is the appliance that takes the most power the one that uses the most energy?

Since $\frac{E}{t} = P$

a little algebra $\Rightarrow$ $$ E = P \cdot t$$ So, for example, if an appliance draws power at a rate of 300 W = 300 J/s, and you run it for 50 seconds, then the energy used is...

$$300\frac{J}{s} * 50\,s = 15,000\text{ J}$$ and $$15,000\text{ J}\times -\frac{\text{1 kJ}}{\text{1,000 J}}= 15\text{ kJ}$$

so Power * time = energy. Which of these is a unit of energy? of power? neither?

kilowatts,     watts / hour,     kiloJoules,     milliJoules / day,     kilowatts * hours

kilowatts - kilowatts means 1000 watts. Just like watts, this is a unit of power
watts / hour - This is energy / time / time: none of power or energy,    
kiloJoules - Joules and kilojoules are units of energy,    
milliJoules / day - This is energy/time, which is power,    
kilowatts * hours - Power * time = energy

Emissions are proportional to energy, not power.

 

table


How much energy do you use (in kWh):

  • if you dry clothes for 1/2 hour?

    5 kW * 0.5 hour=2.5 kWh.

  • How much energy do you personally use if you and a friend have about the same amount of laundry and you throw it together and dry for half hour?

    Each of you uses half of the energy above, so 1.25 kWh each.

  • if you turn on an air conditioner for 10 hours?

    1.6 kW * 10 hours = 16 kWh.

  • if you use a hair dryer for 6 minutes?

    6 minutes is 1/10 of an hour, so 1 kW * .1 hour = 0.1 kWh.

  • How long could you listen to a your stereo (at full volume) before you used as much energy as drying your hair for 6 minutes?

    The power of a stereo is 100 W = 0.1 kW. So, solve 0.1 kWh = 0.1 kW * $x$ hours... $x$ = 1 hour.

  • Which uses more energy...Doing one 1/2 hour dryer run yourself once a week, or watching TV for 1 hour each day?

In many homes the refrigerator is the appliance that uses the most energy over the course of a year. (Eia.doe.gov)

Energy per person

How much electric energy does each person use?

Here is a monthly utility bill from Paul's family of 5 people.

  • What is the cost of 1 kWh of electricity?
  • How many kWh/day did the whole family consume?
  • This is how many kilocalories / day? Then, divide by 2000 kcal/day/person to get the number of "servants" this family employs!
  • How many kWh/day/person?
  • What other forms of energy do you pay for in a home? What kind of appliances use non-electric energy?
  • Does adding up just usage at home capture all the ways this family uses energy? What are other major energy uses?

Compare the cost you found to the costs that Forbes (Jan 2018) claims by 2020 for renewables.

David MacKay suggests that good units to use to think about your personal energy consumption are average energy used per day for one person: $$\frac{\text{kWh}}{\text{person}\cdot\text{day}}$$

Solar power

Could solar power meet our / your household needs?

[There is even more specific information--including average yearly cloudcover and meteorological conditions, and typical system costs--at the National Renewable Energy Lab's pvwatts.nrel.gov website, which you can search by zipcode.]

[That's averaged over a whole day. Of course, all of the energy is generated during the daytime, and most of it when it's sunny outside, not cloudy.]

Current solar photovoltaic (PV) devices convert about 15% (~ 1/7) of the energy that falls on them into usable electricity.

  • Calculate how many square meters of solar panels would be needed to cover the electric usage of Paul's family, with the 15% loss
  • How many square meters per person?

Land use

Is this a ridiculous amount?

Compare this with the land area we as a society have dedicated to another public good: the interstate highway system. It's ~75,000 km long with an average density of 1000 km${}^2$ for every 800 km of length. That's an area of 94,000 square km. Dividing this by the current population of ~300 million, this works out to ~300 square meters of Interstate per person.

Converting units

How many seconds / hour = "seconds per hour" = "seconds in each hour"?

There are 60 seconds in each minute: 60 s/ min.

There are 60 minutes in each hour: 60 min / hour.

"60 minutes in each hour, and 60 seconds in each of those minutes" = 60 min/hr $\times$ 60 sec/min = 3600 sec / hr = "3600 seconds in each hour".

Cost table

  market cost cost per kWh cost per kWh if $\rightarrow$
electricity
coal $40 / ton $0.004 $0.012
natural gas $10 per million cf $0.03 $0.09
gasoline $2.69 / gal $0.09 $0.27
electricity retail from NIPSCO $0.12
solar PV standalone (hybrid) EIA 2026 \$0.029 (\$0.042)
Wind onshore (offshore) EIA 2026 \$0.031 (\$0.115)
AAA battery $1.50 per battery $1000.00

 

Cost of food energy

Dining HallWhat does a kWh worth of food calories cost?

[Writing assignment]

Image credits

Tim Blaum, Elizabeth Albert