Energy and Power (and explosions!)

Transcription

1 Energy and Power (and explosions!) It s hard to say what energy is: we know it when we see it. Feynmann: Ul8mately, energy is the ability to exert a force over some distance. Energy is a conserved quan8ty. This does not sound right to most people. We speak of using energy (like using it up). Actually, we just change its form from useful kinds to less useful kinds. Energy of mo8on, gravita8onal poten8al energy, electrical poten8al energy, many types of chemical energy, nuclear energy are usually very useful. Heat can olen be less useful. (Unless something is out of equilibrium.) One way people think of the end of the universe is when all the useful energy is converted to uniform heat. This may not even be correct, but if it is, it is very far in the future. Do not copy this down. It is online at hop://

2 Units Energy can be measured, and there are many different units. Physicists use the joule named aler James PrescoO Joule. Joule was amazing! It s worth reading about him just to see how such brilliant people change the world.

3 James Prescott Joule FRS (24 December October 1889) was an English physicist and brewer. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him. He worked with Lord Kelvin to develop the absolute scale of temperature, made observations on magnetostriction, and found the relationship between the current through a resistance and the heat dissipated, now called Joule's law. [Wikipedia]

4 Units Since energy represents the ability to exert a force over some distance, its units must be the same as force 8mes distance. Many engineers use foot-pounds for the units of energy. Similarly, a joule is one newton-meter. They are close. One foot-pound is only slightly bigger than a joule. 1 L-lb = J. Just call it even, or 1.4 if you want to be closer. Physicists olen deal with 8ny liole atoms, and need a unit of energy that is very small. We use the electron-volt for that. One electron-volt is approximately the strength of the bonds between atoms in normal crystals. 1 J = 6,242,000,000,000,000,000 ev. (That s 6 quin8llion.)

5 calories calories are a unit of energy usually used to measure heat. A calorie is the amount of heat it takes to heat one gram of water by one degree C. Note, there are 5 grams of water in one teaspoon, so it would take 5 calories to heat one teaspoon of water by 1 degree C. Joule established the equivalence and found the conversion from newtonmeters to calories! (He was the son of a brewer, aler all.) One calorie = joules. Just call it 4.2, or even 4, for rough calcula8ons.

6 calories vs Calories In thermodynamics, one calorie (lower case) is the heat to raise one gram of water by one degree C. Unfortunately, the chemical energy in food is measured in units called Calories. This is unfortunate, because the only apparent difference is the capital C, but the meaning is VERY different. 1 Calorie = 1000 calories Some8mes, food-calories are called kcal (kilocalories). This is a great idea! 1 Calorie (kcal) = 4184 J. (Call it 4000.) Engineers olen use something called the BTU (Bri8sh Thermal Unit). 1 Calorie (kcal) = BTU. (Call it 4.) So, 1 BTU 1000 J.

7 There is a LOT of energy in food! One half ounce of pecans has 100 kcal of energy. (100 food Calories if you like.) That s only about 5 pecans! (10 halves) 1 calorie will raise the temperature of 1 gram of water by 1 degree C. So, 1 kcal (Cal) will raise the temperature of 1000 grams (1 liter) of water by 1 degree C. So 5 pecans has enough energy to raise the temperature of 1 kg of water by 100 degrees C! You could burn half an ounce of vegetable oil and release the same amount of energy, but you would never capture it well enough to heat a quart of water by 100 degrees! Your body is incredibly efficient at capturing the chemical energy in food.

8 A useful unit of energy The jelly donut is a very useful unit of energy: 1 jelly donut = 250 kcal = 1 MJ This is the energy needed to accelerate a car (1 ton) to 100 mph. It is the energy needed to lil a 100 kg man to a height of 1 km. It is the energy needed to run a 100 wao light bulb for 3 hours

9 Comparison of energy sources

10 Power Just as velocity is the rate of change of posi8on (meters per second), power is the rate of change of energy (joules per second). Of course, it depends on where the energy is going to or coming from, but power is always a measure of energy per 8me. 1 wao = 1 joule per second. This is very important. You would never confuse miles per hour with miles, so don t confuse power and energy. Meaningless: How many miles per hour is it to Houston? Just as meaningless: How many waos did you burn on the treadmill?

11 Explosions Ques8on: If TNT has less energy per gram than chocolate chip cookies, or vegetable oil, why is its explosion so more destruc8ve? Answer: Because the energy is released so much quicker. The power is far higher. Consider 1 gram of alcohol burned in 10 seconds. P = (7 Calories)/(10 seconds) = (30 k-joules)/(10 seconds) = 3 kilowaos Consider 1 gram of TNT detonated in 1 microsecond P = (0.7 Calories)( seconds) = 3 gigawaos! (for a very short 8me)

12 DetonaIon vs DelflgraIon Detona8on: Supersonic wave (faster than the signals can be transmioed into the explosive ahead - explosive has no idea its coming). Propagates through shock compression of the explosive. Shock wave heats the explosive, ignites the chemical reac8ons, large energy release. Energy pushes the shock wave on into next bit of explosive. Examples: High explosives. Deflagra8on: Subsonic wave (slower than signals move into the explosive ahead - explosive knows the wave is coming and can adjust to it). Propagates by heat conduc8on. Mass diffusion from the hot burnt products of the chemical reac8on and the cold explosive ahead. Examples: gasoline engines, gunpowder. hops://

13 kilo wal hours Since one wao is one joule per second, you can imagine that one joule is the amount of energy expended when you exert one wao of power for one second. 1 J = 1 Ws (1 joule is one wao-second.) This is like saying 1 mile is 1 mile-per-hour for one hour. Similarly, 3600 J = 1 Wh (one wao-hour) Similarly, 3,600,000 = 1 kwh (one kilowao-hour) KilowaOs are units of power (energy per 8me) KilowaO-hours are units of energy (power 8mes 8me)

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15 Burn Calories, Not Kilowatts Take the stairs!

16 Burn calories, not kilowatts.

17 People use language loosely. ScienIsts must be precise. This can be a dangerous mixture. For example, consider some interdisciplinary research between an economist, a philosopher, and a physicist. The economist says: 8me is money. We write down T = M The philosopher says: knowledge is power. We write down K = P The physicists says: power is work over 8me. We write down P = W/T We can eliminate T by subs8tu8ng M and get: We can eliminate P by subs8tu8ng K and get: P = W/M K = W/M Now we can flip the equa8on and get: M = W/K That is, for any finite amount of work, money tends to infinity as knowledge tends to zero. J

18 Other units of power A horsepower is a very common unit. Surprisingly, horsepower was introduced by James WaO who the wao is named aler. He found that a horse could turn a mill wheel 144 8mes in an hour. This worked out to about 540 foot-lbs per hour. So, one horsepower is 540 foot-lbs per hour. Other conversion: 1 hp = 746 waos. It s easy to round this to 750, or even 1000.

19 Comparison of power scales

20 Electric cars Typical energy efficiency is a liole beoer than 4 miles per kwh. Note that this is miles per kwh instead of miles per gallon. My car gets about 4.3 miles per kwh, but it depends on the wind, air condi8oning, driving style, etc. Compare: gasoline 40 miles gallon versus electric 4 miles kwh Recall that gasoline was about 10 calories per gram. Actually, using precise values this works out to 127 MJ/gallon. Remember 1 kwh is 3,600,000 joules, so gasoline contains 35.3 kwh/gallon. So: 4 miles kwh x 35.3 kwh gallon =140 miles gallon (equivalent)

21 First thing we note: Electric motors are FAR more efficient than gasoline engines! (Somewhere between a factor of three and a factor of four.)

22 Second note: But wait! There is a cheat here. You always have to watch for the cheat. That electricity did not get magically stored into the car baoery. The process of charging a rechargeable baoery is not perfectly efficient. For my car, it is about 80% efficient. So for every one kwh my car baoery supplies to the motors, I had to purchase 1.25 kwh from the electric company. So 140 miles per gallon (equivalent) for the electric car is really more like 115 (that is, 140/1.25). Gasoline does not work that way. You don t lose much gas between the nozzle at the pump and your engine. When you take it all into account, figure a car that gets 40 mpg with gasoline would get about 115 mpg (equivalent) from electric motors.

23 Third note: Recall that one gallon of gas had 34 kwh of energy. But in an electric car, you have to pay for 1.25 kwh for every kwh you use. So, let s compare the price of one gallon of gasoline to 43 kwh of electricity. Roughly, one gallon of gasoline is about $2.50, and 43 kwh of electricity is about $4.70. (YMMV.) So, gasoline is WAY cheaper than electricity. But is it enough to make up for the efficiency of electric motors? Gasoline: Electric: 4 40 miles gallon x1gallon $2.5 miles 1.25 kwh x1 kwh $0.11 =16 miles $ = 29 miles $ Electric cars can be cheaper at todays prices

24 Diet and Exercise Here is a useful conversion: 50 waos 1000 kcal/day If you eat 2000 kcal each day (as I do) then on the average your body consumes 100 waos. This includes exercise and rest. It s the total work you do plus the heat you generate. (You also lose energy by radia8ng (that means glowing) in the infrared, but this is very small.) How much energy do you use in exercise? Remember, one horsepower was 750 waos. Only a highly trained athlete can come close to this. For example, a Tour de France rider will average waos for a four-hour stage.

25 Be careful if you work out in a gym!

26 This can t be right? 565 kcal in 61:45 is 637 waos. That s 0.85 hp! For more than an hour! On the ellip8cal, I can make it say 800 kcal in an hour. That s 930 waos! That s 1.2 hp! For more than an hour! I m a 60 year-old man. I cannot exert 0.8 hp for an hour, much less 1.2 hp. If my body averages 2000 calories in a day, there is no way I can burn 800 in a single hour. Conclusion: the machines are lying! (Why?) Always be willing to ques8on what you are told. Some8mes you won t care, or some8mes you won t be able to tell. Be skep8cal!

27 Recap Force causes mass to accelerate 1 pound 4 newtons (actually 4.45) Energy means a force can act over a distance 1 joule = 1 newton-meter 1 foot-pound 1 kcal 4000 joules (actually, 4184) 1 kwh (kilo-wao-hour) = 3,600,000 joules 1000 kcal Power is rate energy changes or moves 1 wao = 1 joule per second 1000 waos = 1 kwh per hour 1 horsepower 750 waos