Energy Models

To support decisions about our energy systems, we must make quantitative estimates in systems that are too complex to gather complete information.

Units

One joule is the energy delivered by one watt of power running for one second. This unit is often used by scientists.

One kilowatt-hour is the energy delivered by one kilowatt of power running for one hour. This unit is used by electric utilities on consumer bills.

Unit Conversions

Usually when we create an estimation, the dimensions are fixed but we have a choice of what units we use.

It may be simplest to perform the calculation using units that are correct, but not the best for communicating with an audience.

If this is the case we can use a unit conversion to go from the correct but awkward unit to a better unit for communication.

Example

Suppose someone says it is 640,000 inches to drive from SSU to Petaluma. This is correct, but you might not find it helpful. If we know that there are 5,280 feet in a mile and 12 inches in a foot, we can provide a more familiar unit.

640,000\;\textrm{inches} \cdot \frac{1\;\textrm{foot}}{12\;\textrm{inches}} \cdot \frac{1\;\textrm{mile}}{5280\;\textrm{feet}} = 10.1\;\textrm{miles}

Units and Dimensions

Note that a unit conversion has different units on the top and bottom and the same dimensions on top and bottom.

This means multiplying a quantity by a unit conversion changes the units but doesn’t change the dimension.

Common Unit Conversions

1609 meters = 1 mile (length)

1055 Joules = 1 BTU (energy)

3.6 \times 10^6 Joules = 1 kWh

Standard Multiplier Prefixes and Scientific Notation

Often for energy quantities, we use the metric prefixes to express scientific notation.

Rather than say 3.2 \cdot 10^{9} Joules, will say 3.2 GJ, using the G for giga or billion.

In the same way as we have before, we can create conversion factors using the table above.

1\ \textrm{GJ} = 1000\ \textrm{MJ}

\frac{1\ \textrm{GJ}}{1\ \textrm{GJ}}= \frac{1000\ \textrm{MJ}}{1\ \textrm{GJ}}

The fraction on the right can be used the same way a unit conversion fraction can.

10\ \textrm{GJ} \cdot \frac{1000\ \textrm{MJ}}{1\ \textrm{GJ}} = 10,000\ \textrm{MJ}

Scientific Notation	English	SI prefix	Symbol	Mnemonic
10^{24}	Septillion	yotta	Y	yodeling
10^{21}	Sextillion	zetta	Z	zebras
10^{18}	Quintillion	exa	E	expect
10^{15}	Quadrillion	peta	P	patient
10^{12}	Trillion	tera	T	teachers
10^{9}	Billion	giga	G	giving
10^{6}	Million	mega	M	metric
10^{3}	Thousand	kilo	k	knowledge

Unit Conversion Example

How many joules in 100 BTU?

From tables or the internet we find 1 BTU = 1055 Joules.

100 BTU \cdot \frac{1055 J}{1 BTU} \cdot \frac{1kJ}{1000J} = 106 kJ