PHYS2012 emp10_01
ELECTRIC CARS
Why do petrol cars dominate?
Why are hybrid petrol-electric cars becoming more popular?
Why do we not see battery powered electric cars on our roads?
What about capacitors as energy storage devices for electric cars?
What is the future of using ultracapacitors for electric cars?
Below are a few simple models which will give some insight into the above questions. The models are not necessarily accurate ones, but do give “ball-park” results.
PETROL CARS – A LONG DISTANCE JOURNEY
Consider a petrol car going on a non-stop 250 km journey at a constant velocity. How much energy and power does the petrol provide?
Parameters describing the simple model for the journey
Quantity / Symbol / Value / Unit / CalculationMass of car / m / = / 1500 / kg
Distance travelled by car / dx / = / 250 / km
dx / = / 2.50E+05 / m
Time for journey / dt / = / 4.00 / h
dt / = / 1.44E+04 / s
Fuel consumption of car / C / = / 10 / L/100 km / 1L / 10 km
Volume petrol used by car / Vol / = / 25 / L
Vol / = / 2.50E-02 / m3
Density of petrol / / = / 750 / kg/m3
Mass of petrol used by car / M / = / 19 / kg / = Vol
Energy density of petrol / u / = / 46 / MJ/kg
u / = / 4.60E+07 / J/kg
Energy used by car / U / = / 8.63E+08 / J / = M u
Efficiency of heat engine / e / = / 0.30
Energy expended as work done on car / W / = / 2.59E+08 / J / = e U
Average rate of energy usage, power / P / = / 1.80E+04 / W / = W / dt
P / = / 18 / kW
The amount of energy that is needed as useful work to be done on the car for the 250 km journey is 2.6108 J and the average rate at which this energy must be supplied is18 kW. For this journey, only 19 kg of petrol is needed.
PETROL CARS – A SHORT SPRINT
Consider a petrol car going starting at rest and accelerating to 100 km/h in 10 s.
How much energy and power does the petrol provide?
Parameters describing a simple model for theshort sprint
Quantity / Symbol / Value / Unit / CalculationMass of car / m / = / 1500 / kg
Initial speed of car / v0 / = / 0
Final speed of car / v / = / 100 / km/h
= / 27.8 / m/s
Time to accelerate / dt / = / 10 / s
Work done = increase in KE / dK / = / 5.79E+05 / J / = 1/2 m v2
Efficiency of petrol motor / e / = / 0.30
Energy needed from petrol engine / QH / = / 1.93E+06 / J / = dK/e
Power required in accelerating car / P / = / 1.93E+05 / W / = QH / dt
193 / kW
Energy density of petrol / u / = / 4.60E+07 / J/kg
Mass of fuel consumed / M / = / 0.042 / kg / = QH / u
The amount of energy that is needed as useful work to be done on the car accelerating for a short period time is 1.9106 J and the average rate at which this energy must be supplied is 190 kW. For this sprint, the petrol needed is insignificant, 42g.
Petrol is a fantastic fuel from the point of view of its energy density. A lot of energy is released when a small amount of petrol is combusted. However, petrol is a non-renewable resource and as a result of the combustion process, undesirable chemicals (hydrocarbons, NOx, COx) are released into the atmosphere.
To have a better understanding of the claims made about hybrid and electric cars it is necessary to know a little about the physical principles of heat engines used in a petrol and diesel cars.
HEAT ENGINES
A heat engine is a physical device that converts thermal energy to mechanical output. The mechanical output is called work, and the thermal energy input is called heat. Heat engines typically run on a specific thermodynamic cycle.
A heat engine absorbs heat energy QH from the high temperature THheat source, converting part of it to useful work W and delivering the rest QC to the cold temperature TCheat sink. In one cycle of a heat engine, there is zero change in the internal energy Uand using the First Law of Thermodynamics, the work and heat transfers are related by
In general, the efficiency of a given heat engine is defined informally by the ratio of "what you get out" to "what you put in." In the case of a heat engine, one desires to extract work and put in a heat transfer. The efficiency e is given by
The theoretical maximum efficiency emaxof any heat engine depends only on the temperatures it operates between. This efficiency is usually derived using an ideal imaginary heat engine such as the Carnot heat engine
Is it possible to recover all the energy lost and convert it into useful mechanical energy?
Second Law of Thermodynamics: 100% of heat can’t be transformed into mechanical energye < 1
Some energy must be transferred to the cold reservoir to satisfy the Second Law of Thermodynamics.Can’t convert 100% of thermal energy into work.
HEAT ENGINES – OTTO CYCLE
The four-stroke Otto cycle spark-ignition engine is the most common engine used for automobiles today. The purpose of internal combustion engines is the production of mechanical power from the chemical energy contained in the fuel. Each cylinder of the engine contains a piston. The movement of the piston in response to the combustion of the engine produces work. In a four stroke engine, during one cycle, the piston moves through the cylinder four times, each of which is called a stroke. In the first stroke, the intake stroke, the piston travels down the cylinder with the volume increasing and the pressure decreasing which results in air being drawn into the cylinder, and then fuel is added to the air. In the second stroke, the compression stroke, the piston travels up the cylinder to its highest point(smallest volume) compressing the fuel-air mixture. Then combustion occurs - a spark ignites the gases and changes the composition of the mixture, raising the pressure and the temperature to their highest values. In the third stroke, the expansion, or power stroke, the high pressure of the gases push the piston down to its lowest point in the cylinder. This produces the work output of the cycle. In the fourth stroke, the exhaust stroke, the exhaust valve is opened and the pressure within the cylinder is higher than atmospheric pressure, so the exhaust gases leave the cylinder as the piston moves from the bottom to top, pushing those gases out of the exhaust valve.
The theoretical efficiency of the Otto Cycle heat engine is given by
where r is the compression ratio and is the ratio of molar specific heats ()
Vmin and Vmax are the minimum and maximum volumes of the gas enclosed in the cylinder by the movable piston.
Typical operating values for a Otto Cycle heat engine are:
r = 8 = 1.4 TC = 330 K TH = 1800 K
e = 0.56 emax = 0.82
The maximum efficiency for the heat engine based upon temperature difference between the hot and cold reservoirs is 82% for a Carnot Cycle but for an ideal Otto Cycle it is only 56% efficient. However, in driving a real car on the road, the efficiency in delivering useful work in moving the car is only between 20% to 30%.
HYBRID PETROL-ELECTRIC CARS
Why is a hybrid petrol-electric car more efficient than an equivalent petrol powered car?
A hybrid petrol-electric car has a higher efficiency than a petrol-only car because it recovers some of the energy that would normally be lost as heat to the surrounding environment in charging the batteries and energy to charge the batteries during breaking. For example, if the efficiency of a typical petrol-only car engine is 20%, what efficiency could be achieved if the amount of heat loss is halved?
The efficiency of a heat engine is given by
Assuming the heat lost (QC) can be reduced by half, then
The efficiency of the hybrid car is 60% compared to only 20% for the petrol. This increase in efficiency is achieved by recovering 50% of the heat lost.The above is only valid if the energy transferred to the cold reservoir is useful in generating electricity to charge the batteries.
Quotes from
The electricity used in Hybrids is created by an alternator driven by a gasoline engine, using gasoline to do it. Think about this! Instead of burning gasoline in the engine to turn the wheels directly, the gasoline is burned in the engine to turn an alternator to produce electricity which is then put into batteries, where it is then later used to send to electric motors, which then turn the wheels. Now, if all those mechanisms and processes were perfectly efficient, fine, there would be no disadvantage of the complicated sequence, but they all have efficiencies which are well below 100%! Adding in lots of extra processes is NOT really beneficial! The very fact that the SAME gasoline is the initial source of energy, and the SAME turning of the wheels is the final goal, makes this all somewhat bizarre. However, Hybrids DO have one real advantage,in that the gasoline engine can run at essentially constant speed. Normal driving involves the engine running at very different speeds, from idling to flat out, and the Physical laws do not permit devices to have excellent efficiency over such wide ranges of speed. It is amusing that you will hear people tell you a hundred different reasons of why they think Hybrids are spectacularly more efficient than gasoline engines, and they are virtually all totally wrong! Just the fact that a gasoline engine has to run in either case should be a clue. If it can always run at whatever speed where it has maximum efficiency, fine, there can be a real advantage. That is rarely the case in what those "experts" describe!
And manufacturers and even the EPA seem willing to ONLY evaluate Hybrids WHILE the batteries are fully charged and are discharging, where they then can claim really impressive mileage figures. I guess that is not ABSOLUTE deception of potential buyers, but it certainly seems pretty close.
First, it will be WONDERFUL if and when battery-powered vehicles and/or hydrogen fuel-cell-powered vehicles become economically practical. Neither seems very likely during the next thirty or probably fifty years, until and unless some great breakthroughs are found in energy production. Maybe YOU might come up with such a concept some day, but in order to do that, you FIRST need to completely understand the many subjects mentioned and discussed here.
It is certainly true that electric motors have some tremendous efficiency advantages over the common 21% (thermal) efficiency of most cars on the road with internal combustion engines! But, unfortunately, the REST of the picture involves devices and technologies which are not as efficient as the electric motors themselves, specifically the batteries and the methods of charging them.
Sadly, "battery-powered vehicles" and future Hydrogen-powered vehicles, will NOT be the wonderful "energy solution" that people think they will be! People think they are "really efficient" because of no exhaust, etc. That's true, IF you only consider the car itself! (This also applies to the electric operational aspects of hybrid cars.)
People, including the so-called experts, seem to be overlooking a central concept! A battery does not MAKE any electricity, it merely stores it. However much energy or work or power you want to get OUT of a battery, must first get put INTO the battery! This is simply stating a long-known fact in science called the Conservation of Energy! In other words, batteries are not FUEL like petroleum or natural gas or coal. They actually have no fuel at all, and are instead simply STORAGE devices. Hydrogen is actually much the same, as there is no existing supply of hydrogen gas; it must be produced, such as by the electrolysis of water (which requires a LOT of electricity again, very similar to the battery situation). Where promotional displays show the "simplicity" of plugging the car into house electricity, they neglect to note just how much electricity that car is going to suck out of the house wiring!
Watch the TV commercials for the future Chevy Volt car. They brag that it will be able to go 40 miles before ever needing its included gasoline engine to start up to recharge the batteries. They ONLY talk about starting out with FULLY CHARGED batteries, and discharging them to provide the power to move the vehicle that 40 miles. They NEVER mention the necessary fact that EXTERNAL power has to be provided from somewhere to re-charge the batteries! In fact, in interviews, the Executives of General Motors show amazing attitudes and apparent lack of knowledge regarding the central subjects! It was NOT an Engineer that dreamed up the Volt, but an Executive with NO expertise in the needed areas! He simply THOUGHT that since most drivers drive less than 40 miles in each round trip, he THOUGHT it would be a great idea to create a vehicle that could go 40 miles without needing any fuel! His interviews seem to sound like he believes in the Tooth Fairy to re-charge those batteries, and that the ONLY thing GM needs to still do is to improve the performance of the batteries! The GM top executive even described their advanced battery packs as having 16 kilowatts of capacity. Apparently, no GM Engineer ever told him that CAPACITY (or energy) can only be described in kiloWatt-HOURS, which is a unit of energy. To describe ANY battery as having a CAPACITY of 16 kiloWatts is simply meaningless and a statement that shows ignorance of basic facts. (For their information, KiloWatts describes POWER, which is the RATE at which electricity or other energy can be put into or taken out of a battery!) These are "facts" upon which GM is intending to base the entire survival of their company! Wow!
But their commercials are like all others for electric/battery-powered vehicles and also hybrids, an IMPLIED assumption of that Tooth Fairy to re-charge the batteries when no one is looking! As if FREE energy and power can somehow be available by some hocus-pocus.
ELECTRIC CARS – LEAD ACID BATTERIES
Can the energy stored in lead acid batteries be used as means to store energy for an electric motor powered car?
Consider the electric car going on the non-stop 250 km journey at a constant velocity. How many 12 V lead acids batteries are required?
Remember, the amount of energy needed as useful work to be done on the car for the 250 km journey is 2.6108 J and the average rate at which this energy must be supplied is 18kWand only19 kg of petrol was needed.
Can the batteries provide the necessary power for the sprint from 0 to 100 km.h-1?
The amount of energy that is needed as useful work to be done on the car accelerating for a short period time is 1.9106 J and the average rate at which this energy must be supplied is 190 kW.
Parameters describing the simple model for the 250 km journey
maintenance free rechargeable sealed lead-acid
Quantity / Symbol / Value / Unit / CalculationEnergy expended as work done on car / W / = / 2.59E+08 / J
Battery rating / R / = / 8.00E+01 / A.h
Nominal battery voltage / V / = / 12 / V
Mass of battery / M / = / 20 / kg
Volume of battery / Vol / = / 0.013 / m3
Internal resistance / Rint / = / 0.005 /
Max discharge current (for 5 s) / Imax / = / 800 / A
Max charge current / IC / = / 24 / A
Energy density - petrol / upetrol / = / 4.6×107 / J.kg-1
Time for journey / dt / = / 4.0 / h
dt / = / 1.44.E+04 / s
Average voltage / Vavg / = / 11.0 / V
Average current / Iavg / = / 20.0 / A
Average output power / Pavg / = / 220 / W / =Vavg I
Power dissipation - internal resistance / Plost / = / 2.0 / W / = Rint Iavg2
Energy supplied by 1 battery / U / = / 3.17E+06 / J / = Pavg dt
Efficiency of electric motor / e / = / 0.8
Energy required by electric motor / WE / = / 3.23E+08 / J / = W / e
No. batteries required / N / = / 102 / = WE / U
Max power of batteries / Pmax / = / 22 / kW / = N Pavg
Total mass of batteries / Mbatteries / = / 2042 / kg / = N M
Total volume of N batteries / Vbatteries / = / 1.4 / m3 / = N Vol
energy density of a battery / ubattery / = / 1.58E+05 / J/kg / = U / M
Energy density: petrol / battery / = / 290 / = upetrol / ubattery
Charging time for 1 battery / dtcharge1 / = / 3.1 / h / = U /(V IC)
Charging time for N batteries / dtchargeN / = / 13 / days / = N dtcharge1
The energy density (J.kg-1) of the lead acid batteries is much less than that of petrol,
upetrol / ubattery ~ 290 as a consequence for the 250 km journey about 100 batteries are required with a total mass of about 2000 kg which is greater than the mass of the car used in the model. If the mass of the batteries is added to the car, then petrol is an even better choice as an energy source for cars compared with lead acid batteries.The lead-acid batteries can provide sufficient energy and provide the necessary power for the short sprint lasting only 10 s. A battery can supply an enormous current (800 A for 5s) but only for a brief period of time.Another problem with batteries is that they can only be charged and discharged only about 1000 times before they have to be replaced.
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ELECTRICAL TERMINOLGY
In discussing the use of batteries and electric motors we come across the terms current, voltage, resistance, etc, all the time but what do these terms really mean?
What is an electric current?
Often, electric current is simply defined as the movement of electric charge. But this statement is imprecise. We have to be more careful in using scientific terminology.
The flow of charge gives rise to an electric current. The current is defined by the equation
average current
where q is the amount of charge that passes a cross-section in the time interval t. A still better definition is
instantaneous current
Consider a volume of electrons (charge e) moving through a wire of cross-sectional area A, length dx and number density n.For the electrical conduction of electrons in a wire, the electrons drift along at an average speed, vdrift = dx/dt. The current in the wire can be expressed as
the concept of vdrift will be consider in more detail later