Physics in a Nutshell:

• Force=mass x acceleration                               Example: 1 Newton (N) = 1 kilogram x 1 meter/second²
• Work (Energy) = Force x Distance                    Example: 1 Joule (J) = 1 Newton x 1 meter
• Power = Energy/Time                                         Example: 1 Watt (W) = 1 Joule/second
• Energy = Power x Time                                       Example: 1 Joule (J) = 1 Watt x 1 second

Some Metric Prefixes:

 

Common Name	Metric Name	Power of Ten
Quadrillion	Peta	1015
Trillion	Tera (T)	1012
Billion	Giga (G)	109
Million	Mega (M)	106
Thousand	Kilo (k)	103
Thousandth	Milli (m)	10-3

 

Watts:

 

Units
50 milliwatts	Indicator LED
10 watts	LED light bulb (many LEDs combined)
25 watts	Compact fluorescent light bulb (CFL)
100 watts	Incandescent light bulb
1000 watts (1 kw)	Home (on average), or a hairdryer, refridgerator, microwave
500,000 watts (500 kw)	Stationary fuel cell for a large office building
1 million watts =1 megawatt = 1 MW	Utility scale wind turbine; a town (1000 homes)
1 billion watts = 1 gigawatt = 1 GW	Large power plant; a city (million homes)
1000 GW	A country (billion homes)
16 trillion watts = 16 terawatts = 16 TW	Total world primary energy demand
120,000 TW	Solar insolation for Planet Earth
1 Horsepower	746 watts

Energy:

 

Units
Potential Energy (gravitational, near Earth)= m g h;	PE in Joules (J) : m=mass (kg), g=gravitational acceleration =9.8 m/s2; h=height (meters)
Kinetic Energy = 1/2 m v2	KE in Joules (J) : m=mass (kg), v=speed (meters/second)
1 British Thermal Unit (BTU or Btu)=1055 J	1 BTU is the energy needed to raise the temp. of 1 lb of water 1 oF. Also approximately the energy released by burning 1 match head
1 kilowatt-hour (kWh): 3.6 Million Joules	Utility companies typically charge around $.12 per kWh
1 MBTU = 1000 BTU	M is roman numeral for 1000
1 MMBTU = 1 million BTU	MM is roman number for 1 million = 1000 x 1000
1 therm = 100,000 BTU	Approximately equal to the energy in 100 cubic feet of natural gas
1 Mcf = 1000 cf	1 Mcf of natural gas has approximately 10 therms of energy. Utilities charge in the (rough) neighborhood of $12 per Mcf, or about $1.20 per therm.
Calorie	1 calorie = 4.184 Joules (different definitions result in values between 4.182-4.186 J ): The energy needed to raise 1 gram of water 1oC.
Dietary Calorie	1000 calories (4.184 kJ)

Heat:
By definition, heat is any transfer of energy resulting from a temperature difference. There are three common mechanisms of heat transfer:

• Conduction: Diffusion of thermal energy through a substance
• Convection: Heat rising due to buoyancy (natural convection), or through the movement of air caused by other means (forced convection)
• Radiation: All substances radiate at a rate proportional to their absolute temperature raised to the 4rth power.
• Conduction Formula: ΔQ/Δt = Rate of heat flow through an area A = k A ΔT/Δx where k is the thermal conductivity, A is the area, and ΔT/Δx is the temperature gradient (change in temperature/change in distance).
• R-value: Specifies the thermal resistance R for a material, such as wall insulation. Recast the conduction formula with R as follows: ΔQ/Δt = (A/R) ΔT, where R = Δx/k. In the US, R is usually given in (ft²· hour · ^oF)/Btu.
• U-Value: The reciprocal of the R-value.

 

Application	Material	Typical R-values (per 1" thick where thickness not mentioned). Units: (ft2-hour-°F)/Btu
Windows	Still Air	5
	Snow	1
	Single pane of 1/8" glass	1
	Double pane of 1/8" glass	2
	Triple pane of 1/8" glass or low-e double pane	3
Walls	Brick	0.2
	Fiberglass insulation	3
	Polyethelene	3
	Strawbale	1.5
	Urethane foam insulation	5.3
	Cardboard	3
	Blown cellulose	3
	Wood bevel siding	.8
	1/2" gypsum board	.45
	Floors Carpet (with fibrous pad/with rubber pad)	2.0/1.25
	Solid wood	1.56
	Roofs Asphalt shingles	.45

 

Water Heaters:

• Efficiency: .6 (gas); .95 (electric)
• Density of water: 8.3 lbs/gallon; 62 lbs/cf
• Maximum recommended temperature: 125 ^oF

Solar Energy (general):

• "One Sun"=1000 W/m² = 1 kWh/(m² • hr) = 317 Btu/(ft² • hr)
• Derating factor for lattitude tilt as opposed to 2-axis tracker for Burlington, VT: .77
• Annual average sun-hours for Burlington, VT: 5.6
• Lattitude, Burlington, VT: 44.50

PV Conversion Efficiencies:

• 9% (thin-film);
• 13% (traditional crystalline);
• 20% (best crystalline);
• 37% (best triple-junction/concentrator)

PV System Parameters:

• Standard AC to DC derating factor (including effects of inversion, wire losses, panel temperature, etc): .77
• Typical inverter efficiency: 92%
• Typical annual output degradation: 1%

Basic Electricity:

• Unit of charge: The Coulomb (C). One electron has a charge of 1.6 x 10^-19 C.
• Unit of current: 1 Amp = 1 C/s. One amp is therefore a current such that 1 coulomb per second of charge flows past any given point in the wire.
• Note that a coulomb is operationally defined as that such that a current of 1 amp will create a force of 2 x 10^-7 Newton per meter between two parallel wires one meter apart. This way we can obtain a unit of charge via simply mechanical physics units.
• Unit of voltage: 1 volt = 1 Joule / coulomb. A voltage of 1 volt between two points is therefore a situation where it requires 1 Joule of work to move 1 C of charge from one point to the other, or such that 1 C will experience 1 Joule of positive work while traversing the opposite path.
• Ohm's Law (DC): V=I/R or I=V/R or R=V/I. All these are different forms of the same forula. V is in volts, I is in amps, and R is "ohms (Ω)".
• Ohm's Law (AC): V=I/Z or I=V/Z or Z=V/I. Here V and I are complex valued "phasors" in volts and amps, respectively, and Z is the complex valued "impedance" in ohms.
• Power (DC) in watts: P = I V; P = I² R; P=V²/R
• Power (AC): P = I_rms² R = I_rms V_rms cos(φ); φ= power factor; R = |Z| cos(φ)
• "rms values" (root-mean-square values): I_rms =.707 I_peak; V_rms =.707 V_peak; V_rms for US wall sockets = 120 V.
• Capactors: Stored charge Q = CV, where C is in Farads (F); Energy stored = (1/2) C V²

Carbon Emissions:

• Coal: 2.3 lb CO₂ per kWh
• Natural Gas: 11 lbs of CO₂ per therm (100 cf)
• Propane: 13 lbs of CO₂ per gallon
• Crude Oil: 697 lbs of CO₂ per barrel
• Gasoline: 20 lbs of CO₂ per gallon

Energy Content of Fuels/Batteries:

• Gasoline: 36 kWh/gallon
• Coal: 4.4 kWh/lb
• Crude Oil: 40 kWh/gallon (there are 42 gallons per barrel).
• Natural Gas: .506 kWh/cf
• Uranium: 1.02 x 107 kWh/lb
• Ethanol: 22 kWh/gallon (LHV); 25 kWh/gallon (HHV)
• Biodiesel: 37 kWh/gallon
• Lead-acid batteries: 35 watt-hours/kg
• Nickel-metal-hydride: 80 watt-hours/kg
• Lithium-Ion: 150 watt-hours/kg

Biomass:

• 1 Hectacre=10,000 square meters = 2.47 acres
• 1 km² = 100 Hectacres = 247 acres
• Cord of wood: 4 ft x 4 ft x 8 ft (including air space), approximately 2400 lbs, or 1.2 tons
• Energy content of wood = 15 GJ/ton (20% moisture), 20 GJ/ton (bone dry)
• Ethanol Yield: 370 gallons/(acre-year)
• Algae-biodiesel: 10,000 gallons/(acre-year)
• Forest biomass: 1 ton/(acre-year); 4500 Btu/lb (dry)