Tools

Energy Models

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

Power and Energy

Power is the rate of conversion of energy.

This means that energy is the product of a power and a time.

$E = P \cdot t$

Usually, we make the estimation that the power is constant over the time period.

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.

Example

If we have a 50 watt laptop running for a short 100 second video we find the energy used by

$E = P \cdot t$

$E = 50\ \textrm{watt} \cdot 100\ \textrm{sec} = 5000\ \textrm{joules}$

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

Density

A density converts a mass to a volume or a volume to a mass.

Material	Density(g/cubic centimeter)
Crude Oil	~0.9
Water	1.0
Air	0.0012
Gasoline	0.740

Example

If we have 2 liters of gasoline (2000 cubic centimeters) the mass of the gasoline is

$2000\ \textrm{cubic centimeter gasoline} \cdot \frac{0.740\ \textrm{gram gasoline}}{1\ \textrm{cubic centimeter gasoline}} = 1.48\ \textrm{kilograms gasoline}$

Energy Density

Gravimetric Energy Density

This is the quantity of energy is released by the conversion (often combustion) of a given mass of the material. Here is a table of the gravimetric (mass) energy densities for a few popular energy storage sources.

Material	Energy Density (MJ/kg)
Gasoline	45
Crude oil	42--44
Natural gas	33--37
Coal	12--31
Wood	14--16
Lithium Battery	0.5

Units and Dimensions

An energy density has different dimensions and different units on the top and bottom. The dimensions of a mass energy density are energy over mass.

This means multiplying by an energy density changes the dimension of a quantity unlike a unit conversion.

Energy Density (Volumetric)

This is the quantity of energy that is released by a given volume of the material.

Carbon Intensity

These are averages for the carbon intensity of electricity for some power plants.

Fuel Source	Carbon Intensity
Coal	2249 lb CO2/MWh
Natural Gas	1135 lb CO2/MWh
Proposed EPA Limit	~ 1100 lb CO2/MWh

Gasoline Usage in the United States

Imagine that we did not have the US Energy Information Administration compiling statistics of gasoline usage. If we needed to make an estimate of gasoline usage to support a decision about the speed limit of fuel consumption how would we make it?

Carbon Intensity of Electricity

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.

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