Week 6

Focus on energy

Energy chapter from Physics for Future Presidents


Note our reading for last week has questions at the back.


The table in the reading provides a direct value for the energy content of each material listed.  The total amount of energy stored in the form that can be accessed by some process.  For example the bullet has all its KE listed but possible gravitational potential energy is not included in the table.  If the bullet were made of U-235 its KE would appear the same but the additional energy that could be derived from nuclear fission would not be included. Most of the energy in the table is held as a form of chemical energy that can be released by burning the material.



The reaction above is not carried out using single molecules.  What on does is combust a specific mass of hydrogen gas and oxygen.  For the table the experiment might involve carefully measuring out one gram of hydrogen.  As stated one way to measure energy content is to carry out the reaction so that the energy released causes a measurable change in temperature. So if this energy could be used to heat up a known amount of water then the temperature of the initial and final system and the mass of water could be measured and the thermal energy change calculated.


Let us consider the bullet.  Here the energy is in a form that in principal one could use to do useful work.  Let us use the bullet to lift a block.


hyperphysics.phy-astr.gsu.edu/ hbase/balpen.htm





Conservation of momentum


immediately after the bullet imbeds in the ball.


This KE is then used to lift the ball.

Energy conservation

Here all of the KE is turned into PE.  The final height of the block can be related to the initial velocity of the bullet with the above result.


Let us calculate the initial KE of the bullet and the KE of the bullet plus block.

For illustration imagine that the big block is 9 times larger that the bullet.


So given the height that the block lifts I can calculate the intial KE of the bullet but only part of that energy went to perform the useful work of lifting.  One can see that to get a higher return on the process simply reduce the mass of the block.  In the limit of zero mass which is the same as shooting the bullet straight up all of the KE is transferred to PE. 

Is this a violation of energy conservation ?   NO!

The block heats up in the process.  Some of the energy is transferred to thermal energy and energy conservation remains intact.




This problem illustrates energy transfer. It shows that the process may not always convert the initial energy into the form that is desired.


Perhaps one can find a process where all the available energy is harvested to perform the desired function (e.g. push a car down the highway).


The problem is that some energy is not in a form that can be completely used.  For example the air molecules in the room  are moving in a random way but their total KE can be calculated and is related to the temperature of the room.  I can therefore easily find out how much energy is available in the form of KE of the air.



This is actually a very tricky problem.  At the microscopic level (Maxwell’s daemons) a daemon should be able to extract the KE from each moving air molecule and use it.  Very careful thinking about the problem however shows that the daemon must use energy in order to extract the energy in the room.  No mechanism can be found that can get at all the energy without expending some.


For thermal processes this is the limit.  The theoretical best efficiency that one can reach.



Not all motors are thermal.  Electric motors for example convert electrical potential energy into perhaps car KE. Here the problems are practical and not theoretical because there are always losses due to friction.  This is one reason that maglev trains are of so much interest.  The practical limits are much lower for this type of locomotion.


In deciding the value of an energy source the process that harvests the energy is an important consideration. For gasoline the method (internal combustion engine) relies on thermal processes.  The gas is burnt creating a very hot gas (spark plug ignites gas air mixture).  The host gas pushes a piston transferring thermal energy to KE of the rotating engine. Some of the energy is lost as heat (either in the engine block or the hot vented gas).


Honest evaluation of energy sources requires consideration of


Practical efficiency and the theoretical efficiency.


In the comparison of hydrogen and gasoline, hydrogen is awarded a higher efficiency.  This is because the energy conversion is very different. Hydrogen is not burned and then the thermal energy extracted.  A fuel cell uses different chemistry to use the energy in hydrogen to separate positive and negative charges.  The energy is directly converted to electrical energy.  If one looks in detail at batteries, chemistry is used to push electrical charges onto the battery ends (separate charge). This process has a much better efficiency but there are still practical limits. 


Typical fuel cell

Internal combustion engine

Battery – electrical motor

50%   max=85%



























The oildrum

The all electric car powered by renewable wind electricity

ERoEI for wind ~ 20, efficiency factor = 0.95

Grid transmission losses = 0.9

Battery efficiency = 0.97

Motor efficiency = 0.92

Combined efficiency = 76.3%


Gasoline internal combustion engine (ICE)

Procuring oil, ERoEI = 30 (assumed), efficiency = 0.967

Refining and transport losses = 0.9
ICE efficiency = 0.4

Combined efficiency = 34.8%

Hydrogen fuel cell

The calculation is based on producing hydrogen from electrolysis of water using wind power electricity and is based heavily on an analysis by Ulf Bossel (reference at end).

Wind power, as for all electric car = 0.95

Losses due to electrolysis of water = 0.7

Compression of hydrogen = 0.9

Losses during distribution = 0.9

Losses during hydrogen transfer = 0.97

Fuel cell efficiency = 0.5
Motor efficiency = 0.92

Combined efficiency = 24%

Bio-ethanol internal combustion engine

ERoEI for temperate latitude ethanol ~ 1.5, efficiency = 0.33

Processing and delivery (estimate) = 0.95
ICE efficiency = 0.4

Combined efficiency = 12.5%



Power usage

California is large, and on a hot day it uses 50 GW,  so it needs the equivalent of about 50 large electric power plants.

A typical large power generating station produces electric posera at a rate of about one gigawatt = one billion watts = 109 watts = 1 GW

Solar cell 15% conversion  1m-m = 1 kWx .15=150 W

A gigawatt, the output of a typical nuclear power plant, would take 2.5 square kilometers of solar. California has a typical peak power use (during the day, largely to run air conditioners) of about 50 gigawatts of electrical power; to produce this would  take 125 square kilometers of solar cells. This would take less than one  thousandth--that’s one tenth of one percent--of the 400,000 square kilometer area of California.

Good cell 40% eff. 2.5 mm for 1 hp, car needs 50-400 hp

Person can generate 0.14 hp  Athelete .67 hp






1 watt

 1 joule per second


100 watts


light bulb, heat from asitting person




1 Hp


typical horse, person running up stairs







1 kW

~1 Hp

small home elctrical needs, power in sun on 1 meterxmeter




100 hP


small car


1 megawatt (MW) 1 million (106) watts


1 MW


 electric power for a small town


45 megawatts  747 airplane;


45 MW


small power plant, 747 airplane




1 gW


large power plant


400 gigawatt


400 gW

= 0.4 terawatts  average electric power use US

average electric power use US




2 terraW


average wordl power consumption


more precise value: 1 hp = 746 watts



more precise value: 1 kW = 1.3 hp



more precise value: 100 hp = 74.6 kW