Energy Conversion Basics

Energy is "a fundamental entity of nature that is transferred between parts of a system in the production of physical change within the system" (Merriam Webster, 2013). Using Sir Issac Newton's definitions, energy is the ability to do work, and work is the result of force moving something over a distance (Goldemberg and Lucon, 2010, 4). Energy is fundamental not only to physical processes but also to biological life itself.

Power is the rate of flow of energy. Power is measured as the amount of energy that is flowing through a system during a period of time.

Energy is an amount. Power is a rate of flow.

Energy comes in many forms: light, heat, movement, electricity, etc. Energy is stored as potential energy. For example, photosynthesis is a biological process that stores solar energy in the carbohydrates that make up a plant. When that plant is burned, that stored energy is released as heat energy.

Measuring Power and Energy

There are different units used for measuring power and energy in the different forms they can take:

Form Power (Rate of Use) Energy (Amount of Use)
Heat Watt Joule
British Thermal Unit
Motion (Kinetic) Horsepower Foot-Pound
Electricity Watt
Kilowatt
Megawatt
Watt-Hour
Kilowatt-Hour
Megawatt-Hour
Light Lumen Lumen-second
Food Calories per Day Calorie
Kilocalorie
Fossil Fuels (Potential) Barrels per Day Gallon of Gasoline Equivalent
Barrel of Oil Equivalent
(BOE - Petroleum)
Thousand Cubic Feet
(Tcf - Natural Gas)
Tons / Tonnes (Coal)

If we have a power rating for a device, we can calculate how much energy that device uses over a given period of time.

For example, a 60-watt light bulb burning for eight hours:

60 watts * 8 hours = 480 watt-hours

Converting Between Forms of Energy

The thermodynamic principle of conservation of energy recognizes the equivalence of heat and mechanical work (Fermi 1937). Conversion between forms of energy is a fundamental task performed by both machines and living organisms. While energy from different sources is often not interchangeable (e.g. solar-generated electricity cannot currently be used to power commercial jet airliners), technological and social adaptation can often permit significant levels of substitution (e.g. trains replace airliners).

Smil Energy Conversion Matrix
Energy Conversions (Smil 2008, 14)

Measurements of energy in different forms and from different sources can be converted to common units for rough comparison. In this paper, the common unit for measuring amounts of energy is the British Thermal Unit (BTU), which is equivalent to the amount of heat needed to raise the temperature of one pound of water at sea level by one degree Fahrenheit. The following are examples of the amount of energy needed for some specific tasks:

Energy Task
300 BTU Typical fully charged laptop battery (14.8V / 5850 mAh)
2,000 BTU Brew a single pot of coffee
125,000 BTU Energy in one gallon of gasoline
950,000 BTU Drive from St. Louis, MO to Kansas City, MO (247 miles) in a 30 MPG Toyota Camry
2 million BTU Drive from St. Louis, MO to Kansas City, MO in a 15 MPG Lincoln Navigator SUV
3 million BTU Burn a 100W light bulb continuously for a year
22 million BTU Drive a loaded 40-ton GCW tractor trailer between Iowa City, IA to New Orleans, LA (1,000 miles, 6 MPG)
75 million BTU World per capita annual primary energy use (BP 2015)
113 million BTU Average annual electricity use in an American home in 2009 (EIA, 2010f)
302 million BTU US per capita annual primary energy use (BP 2015)
98 quadrillion BTU (98 quads) Total US primary energy use (BP 2015)
549 quadrillion BTU (549 quads) Total world primary energy use (BP 2015)

Because the BTU is a fairly small unit, large-scale energy usage figures from government literature are commonly given in quadrillion BTU, or quads. Although various scales of Joules (MJ, EJ, etc.) are commonly used in scientific literature to conform to the International System of Units, BTUs are used in this document to eliminate unnecessary mental transformation when referencing source documents. Since American total energy use has hovered around 100 quads since the mid 2000s, use of quads also facilitates quick mental calculation to percents. Quads are also fairly close to exajoules (1 quad = 1.055 EJ), so there is a rough interchangeability with literature that uses exajoules.

Listed below are some theoretical conversion factors between different energy measurement units:

Source Destination Conversion Factor
1 BTU 1,055 Joules
1 Quad 1.055 Exajoules
1 Quad 1,000,000,000,000,000 BTU
1 Kilocalories (heat) 3.966 BTU
1 Foot-pound (kinetic) 0.0012851 BTU
1 Lumen-hour (light) 0.005 BTU (Atkinson et al 2007, 12-28)
1 kWh (electricity - 100% efficiency) 3,412 BTU
1 horsepower for one hour 2,500 BTU
1 kWh (electricity - thermal conv. factor 33%) 10,339 BTU (Davis et al 2015, B-6)
1 Megaton TNT (destructive power) 3.9 T BTU (Hall et al 180)

Heat Content of Different Fuels

The table below summarizes conversions between units and typical heat values representing the energy capacity of various fuels:

Petroleum
1 Tonne of Oil Equivalent (Toe) 42,460,000 BTU
1 Barrel Petroleum (EIA 2010e) 5,800,000 BTU (gross)
1 Gallon of Diesel (Davis et al, 2015) 138,000 BTU (gross)
1 Gallon of gasoline (Davis et al, 2015) 125,000 BTU (gross)
1 Gallon of ethanol (Davis et al, 2015) 84,600 BTU (gross)
1 Pound of Jet A Fuel (EIA 2015; Imperial Oil, 2015) 20,260 BTU (gross)
Natural Gas
1 Cubic Foot Dry Natural Gas (EIA 2015, A-4) 1,032 BTU
1 Therm Natural Gas 100,000 BTU
1 Trillion Cubic Feet (tcf) Natural Gas 1.032 Quads
Coal
1 ton coal - US Avg. 2009 (EIA 2011b) 19,973,000 BTU
1 ton anthracite coal (EIA 2011b) 22,000,000 - 25,000,000 - 28,000,000 BTU (low,avg,high)
1 ton bituminous coal (EIA 2011b) 21,000,000 - 24,000,000 - 30,000,000 BTU (low,avg,high)
1 ton subbituminous coal (EIA 2011b) 17,000,000 - 17,500,000 - 24,000,000 BTU (low,avg,high)
1 ton lignite coal - high (EIA 2011b) 9,000,000 - 13,000,000 - 17,000,000 BTU (low,avg,high)
Nuclear
1 lb Uranium (WNA 2015b) 166 MM BTU
Biomass
1 lb. dry wood (Foote 2013) 8,600 BTU (gross)
1 cord (1.25 tons) fuel wood (EIA 2015, Table D-1) 20,000,000 BTU (gross)
1 lb. agricultural residue (moist) 4,300 BTU
1 lb. agricultural residue (dry) 7,300 BTU
1 bushel of corn (EIA 2012, 330) 392,000 BTU
1,000 cubic feet softwood (Haynes 1990) 248,000,000 BTU
1,000 cubic feet hardwood (Haynes 1990) 320,000,000 BTU

Efficiency

Although conversion between measurement units is generally trivial, the transformation between physical availability of fuel and energy involves uncertainty due to variations in fuel constitution and energy density, as well as often significant losses in different conversion processes.

For example, most fossil fuels are burned with useful kinetic energy released as a by-product of generated heat. As such, with current technologies, much of the potential energy in fossil fuels and biomass is lost as waste heat sent up cooling towers or vented in radiators.

Efficiency is the amount of the input energy that actually comes out in some useful form. Efficiency of power convertors covers a wide range:

There are two heating values that can be given for fuel combustion. A High (gross) value considers the energy that vaporizes the water resulting from combustion. A Low (net) value ignores that energy. Low values are commonly used reports from Europe. High values are used by the US Energy Information Administration and this document follows that convention in using high heating values (EIA 2015).

When performing conversions involving fossil-fuel electricity plants, efficiency is often expressed in terms of heat rate, which is the amount of heat contained in the input fuels (coal, natural gas, or oil) needed to generate one kilowatt (kW) of electricity sold to consumers. In 2015, the average heat rate for power plants in the USA was 10,495 BTU needed to generate 1 kilowatt (kW) of electricity.

Note that this is only around 1/3 of the theoretical amount of BTUs in one kilowatt of electricity, meaning US fossil-fueled power plants have an average efficiency (thermal conversion factor) of only around 33%. One third of the energy that goes in to power plants leaves as wasted heat going up smokestacks and cooling towers.

Capacity and Load Factors

All energy sources (especially renewables) have some level of intermittency. Coal-fired generators must be taken off-line occasionally for maintenance. Solar power is not generated at night and wind power is unavailable when the wind slows or stops blowing.

Capacity factor is the percentage of the rated maximum potential power that a system creates over time under real-world conditions. Capacity is an especially important consideration with renewable energy generators, with hydroelectric dams having capacity factors as high as 80% and wind farms having capacity factors as low as 20% (RERL 2011).

A related concept is load factor, which represents how effectively a system's capacity is utilized by customer demand. Capacity factor focuses primarily on supply while load factor represents the level of harmony between supply and demand.

Load factor is commonly use in transportation to measure the percent of maximum capacity used on an average basis, such as the average percentage of seats occupied on an airplane). A car with four seats but carrying only a solo driver has a load factor of 25%. Transportation system operators strive to increase their load factor to increase profits.

Resources vs Reserves

In looking at estimates for the amount of a resource that is available, it is important to distinguish between three different ways of looking at a resource.

These figures can change due to improvements in technology, changes in accounting standards, or increases in resource prices that make previously inaccessible resources economically viable. Adding to the uncertainty of these figures are commercial or political considerations that provide incentives to overstate or understate reserves. For example, OPEC production quotas are based on a country's reserves, which provides an incentive for countries to overstate their reserves.

Conversion Examples

News reports of energy resources often present large numbers that make those discoveries seem quite significant. However, when placed in the context of resource consumption, the results can be much more sobering.

Unit Conversion Using Unit Cancellation

Calculations and analysis involving energy and power commonly involve conversions between units, and these conversions can become complex as they go through multiple steps.

One way of keeping track of these steps is Unit Cancellation, where units are written as sequences of fractions, and matching units on the tops and bottoms of these fractions cancel each other out to reach a desired end unit.

Given the light-bulb example above, suppose we want to know the amount of energy used by the bulb in kilowatt-hours (which is the unit normally used to buy electricity) and the cost to run that bulb for that period of time.

Each kilowatt-hour represents 1,000 watts. First we set up the equation:

480 watt-hours   1 kilowatt-hour
-------------- * ---------------
       1         1000 watt-hours

Cancelling watt-hours, we get:

480 watt-hours   1 kilowatt-hour
-------------- * --------------- = 0.48 kilowatt-hours
       1         1000 watt-hours

Tacking on a typical total cost of 25 cents per kilowatt-hour, cancelling, and multiplying through:

480 watt-hours   1 kilowatt-hour        $0.25
-------------- * --------------- * --------------
       1         1000 watt-hours   1 kilowatt-hour


480 watt-hours   1 kilowatt-hour        $0.25
-------------- * --------------- * -------------- = $0.12
       1         1000 watt-hours   1 kilowatt-hour

As another example, suppose we have a flashlight that uses three 2.4 watt-hour AA batteries and a 100-milliwatt LED bulb. We would like to know how long that flashlight can be used on each set of batteries.

First we set up the conversions:

3 batteries    2.4 watt-hour   1 flashight
------------ * ------------- * -----------
1 flashlight     1 battery      0.1 watts

Cancelling out the units and multiplying through:

3 batteries    2.4 watt-hour   1 flashight
------------ * ------------- * -----------
1 flashlight     1 battery      0.1 watts


3 batteries    2.4 watt-hour   1 flashight
------------ * ------------- * -----------
1 flashlight     1 battery      0.1 watts


3 batteries    2.4 watt-hour   1 flashight
------------ * ------------- * ----------- = 72 hours
1 flashlight     1 battery      0.1 watts

Note that this is an optimal value. Actual batteries often provide less than their rated capacity depending on the type of load and environmental conditions.

Resources In Terms of Annual Consumption

For example, various estimates ( USGS 1999, USGS 2013) put the amount of technically recoverable oil resources in the environmentally-sensitive (and politically-controversial) Arctic National Wildlife Refuge (ANWR) at around 10 billion barrels.

For context, the US Energy Information Administration reported that the United States consumed around 19.4 million barrels per day. Oil production and consumption is commonly reported in barrels per day rather than by year.


19.4 million barrels   365 days   7.1 billion barels
-------------------- * -------- = ------------------
      day                year		year


10 B barrels             1 year		         1.4 years
------------ * ------------------------- = --------------------
  resource     7.1 B barrels consumption   US total consumption

So, you can make the case that placing that area at environmental risk in exchange 17 months of US consumption is a dubious proposition. And since US oil consumption will likely increase, and not all of that 10 billion barrels can be assured to be economically feasable to extract, the number is likely lower.

However, oil cannot all be sucked out of the ground at once, and the rate of production can be used to estimate how long a resource will last (the reserves-to-production ratio). For example, if production could be ramped up to two million barrels per day:

10 B barrels   100 MM          1 day         1 year      13.7 years
------------ * ------ * ----------------- * -------- = --------------
  resource      1 B     2 MM barrels prod   365 days   prod from ANWR

And, given a price for oil of $54/barrel (on 1/6/2017):

10 B barrels      $54        $540 B revenue
------------ * -------- = -------------------
  resource     1 barrel   from total resource

While a significant amount of that would be involved in paying the costs of exploring and extracting that oil, half a trillion dollars is indeed alot of revenue for an oil producer, and is a significant incentive.

Energy = Power * Time

Electrical generating resources are commonly specified in terms of the flow of energy (power) rather than the amount of energy.

Electrical power is commonly expressed in kilowatts (thousands of watts) or megawatts (millions of watts).

An amount of electrical energy is commonly expressed in kilowatt-hours or megawatt-hours. One kilowatt of energy flow for one hour is a kilowatt-hour. When you pay your home electrical bill, the amount of electricity you use is usually given in kilowatt-hours.

For example: Contemporary wind turbines are commonly rated at two to three megawatta apiece. The wind does not blow constantly, so a turbine cannot consistantly generate its peak power. Utility scale wind turbines had a capacity factor of 32% in 2015, meaning that on average they only generated around 32% of their rated power.

Therefore, for one turbine over a year:

     2 MW to 3 MW        32% capacity factor   365 days   24 hours    5,600 to 8,400 MWh
---------------------- * ------------------- * -------- * -------- = ---------------------
1 turbine rated power    average over a year    1 year     1 day     1 turbine over a year

Using the BTU common unit, it is possible to compare the amount of energy used or produced in different forms. For example, in 2015 in the US, it took a coal-fired plant around 10,495 BTU to generate 1 kilowatt (kW) of electricity (the heat rate). Given that heat rate, each wind turbine can generate the equivalent of:

 5,600 to 8,400 MWh     1000 kW   10,495 BTU heat rate   59 B to 88 B BTU
--------------------- * ------- * -------------------- = ----------------
1 turbine over a year    1 MW       1 kW electricity       over a year

In 2015, the US used around 97 quadrillion BTU (quads) of primary energy for all activities. So to estimate the number of wind turbines needed to convert the US entirely to wind power:

97 quads total    1,000,000 billion BTU   1 turbine over a year   1.2 to 1.6 million turbines
--------------- * --------------------- * --------------------- = ---------------------------
1 year total US          1 quad            59 B to  59 B BTU            Total US demand

Provided you could find windy locations to install all those turbines, and given a cost of $3 to $4 million to install each turbine:


1,200,000 to 1,600,000 million turbines   $3,000,000 to $4,000,000       $3.6 to $6.4
--------------------------------------- * ------------------------- = ------------------
           Total US demand                installation cost/turbine   Total capital cost

In 2015, the US gross domestic product (total economic activity) was around $18 trillion. And while all those turbines would not be installed in one year, anyone proposing a major conversion of US energy to wind needs to also indicate how that conversion will be paid for.

Human Energy

While high-performance athletes can work at levels up to 2.5 horsepower for brief spurts, over extended periods, humans can only generate the equivalent of 0.1 to 0.3 horsepower over extended periods:

0.1 to 0.3 horsepower    2,500 BTU      250 to 750 BTU
-------------------- * ------------ = ------------------
 1 human over a day    1 horsepower   1 human over a day


250 to 750 BTU    8 hours     2,000 to 6,000 BTU
-------------- * ---------- = ------------------
 1 farm worker   1 work day   1 farm worker day


    125,000 BTU        1 farm worker day    21 to 63 days human labor
-------------------- * ------------------ = -------------------------
1 gallon of gasoline   2,000 to 6,000 BTU    per gallon of gasoline!

Going in the other direction, A drive from Spokane, WA to Missoula, MT in a 30 MPG compact sedan is around 200 miles:

     200 miles        1 gallon gasoline       6.7 gallons
------------------- * ----------------- = -------------------
Spokane to Missoula       30 miles        Spokane to Missoula


    6.7 gallons       21 to 63 days human labor   140 to 420 days human labor
------------------- * ------------------------- = ---------------------------
Spokane to Missoula      1 gallon of gasoline        Spokane to Missoula


This does not consider the energy used in the manufacture of the car,
construction or maintenance of the highway, etc.

Efficiency

In considering efficiency, a conventional 60-watt incandescent light bulb is rated at emitting 800 lumens. Leaving that light on for an hour:


 800 lumens    1 hour    0.005 BTU     4 BTU light energy
------------ * ------ * ------------ = ------------------
1 light bulb   1 hour   1 lumen-hour   1 light bulb hour


  60 watts     1 hour    3.412 BTU    205 BTU electricity
------------ * ------ * ----------- = -------------------
1 light bulb   1 hour   1 watt-hour    1 light bulb hour


4 BTU light energy
------------------------- = 0.02 = 2% efficiency
205 BTU electrical energy


The other 98% of the energy is released as heat

An equivalent compact florescent bulb emitting the same amount of light would use around 15 watts:

 800 lumens    1 hour    0.005 BTU     4 BTU light energy
------------ * ------ * ------------ = ------------------
1 light bulb   1 hour   1 lumen-hour   1 light bulb hour

  
  15 watts     1 hour    3.412 BTU    51 BTU electricity
------------ * ------ * ----------- = ------------------
1 light bulb   1 hour   1 watt-hour    1 light bulb hour


   4 BTU light
------------------ = 0.08 = 8% efficiency
51 BTU electricity


Compact florescent bulb is 4x as efficient as comparable incandescent

Time-Space Compression

A further consideration should be given to the difference between conversion efficiency and use efficiency. Modern jet airplanes use a tremendous amount of fuel, but they are actually quite efficient in terms of the amount of energy needed to transport a single person for a single mile (passenger-mile).

For example: On a 2011 vacation to Israel, I flew a Boeing 777 between Atlanta and Tel Aviv. On disembarking at both ends, I asked the pilots how much fuel we had used in pounds:

  ATL -> TLV = 240,000 pounds of Jet A fuel
+ TLV -> ATL = 465,000 pounds of Jet A fuel
----------------------------------------------
= 465,000 lbs of fuel


 465,000 lbs fuel    1 ton       233 tons fuel
------------------ * -------- = ------------------
Round trip ATL/TLV   2000 lbs   Round trip ATL/TLV


465,000 lbs-fuel     20,260 BTU   9.42 trillion BTU
------------------ * ---------- = ------------------
Round trip ATL/TLV   1 lb fuel    Round trip ATL/TLV


9.42 trillion BTU        125,000 BTU        75,400 gal gasoline equivalent
------------------ * -------------------- = ------------------------------
Round trip ATL/TLV   1 gallon of gasoline        Round trip ATL/TLV

The trip was a total of around 12,800 statute miles:

12,800 miles 
÷ 75,400 gallons 
----------------------------------------------
0.17 miles-per-gallon-equivalent for a B777

The B777 holds around 300 passengers and both of my flights were full:

300 passengers      12,800 miles      Round trip ATL/TLV     51 passenger-miles
-------------- * ------------------ * ------------------ = ----------------------
  1 Aircraft     Round trip ATL/TLV   75,400 gal gas eq.   1 gallon gas eqivalent

Since the typical compact sedan gets around 30 MPG, taking a B777 is more energy efficient than driving alone in a typical compact sedan.

This is a demonstration of the geographic phenomenon referred to as Time-Space Compression (Harvey, 1990, 240-307). Humans generally perceive the length of travel in terms of time (or financial expense) rather than in terms of distance. Technology has permitted humans to harness fossil energy and move very quickly (both on land and in the air), so the perceived distance of my Israel trip was actually quite short. The equivalent trip 300 years ago by sailing ship would have taken weeks and would have been a complex, expensive and dangerous endeavor.

One significant implication of time-space compression is that although developed countries often use energy efficiently in thermodynamic terms, they tend to use more energy in total than developing countries. The flip side of that is the use value of a gallon of Diesel to a farmer in the developing world (such as to get crops to a local market) is greater than the use value of that same gallon to an American (who would use that same gallon only to move a truck of lettuce six miles on its way from California). This is referred to as marginal value.

Total Annual Energy Consumption

Depending on the source, the Americans use three to five times the amount of energy on a per capita basis than the global average.

  Annual Amount BTU Per Capita US % of World
World Primary (BP 2015)   549 Quads 75 MM BTU  
US Primary (BP 2015)   98 Quads 302 MM BTU 18% of world
World Oil (BP 2015) 33.6 B Barrels 195 Quads 4.6 Barrels  
US Oil (BP 2015) 6.95 B Barrels 40 Quads 21.5 Barrels 21% of world
World Natural Gas (BP 2015) 120 Trillion Cubic Feet 126 Quads 16,400 Cubic Feet  
US Natural Gas (BP 2015) 26.8 Trillion Cubic Feet 26.4 Quads 83,000 Cubic Feet 21% of world
World Coal (BP 2015) 9,000 MM tons 167 Quads 1.23 tons  
US Coal (BP 2015) 998 MM tons 21.6 Quads 3.1 tons 11% of world
World Electricity (BP 2015) 23,500 tWh 243 Quads 3.2 MWh  
US Electricity (BP 2015) 4,300 tWh 44.4 Quads 13 MWh 18% of world
World Population (USCB 2015) 7,296 MM      
US Population (USCB 2015) 323 MM     4.4% of world
EIA Sankey Diagram
US Energy Flow, 2015 (EIA 2016)