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Great Ideas in Science: Physics

Einstein’s three ideas in 1905 Why should I care?

Because those ideas changed the way we live now! How?

Science of global warming

The idealized scientific method:

• Based on proposing and

testing hypotheses

• hypothesis = educated guess

• In Mathematics, you start

with Axioms: A self-evident

and necessary truth (Webster

Dictionary) 自明之理

The Scientific Method

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Energy and Entropy

Why is this important? 1. A/C in the summer

2. Nuclear Energy – what happened in Fukushima following the earthquake and tsunami.

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What is Energy? What is Heat?

• Energy is “the capacity to do work”.

– The energy to lift an object of 1 kg up by 10cm is about 1 joule (J).

• Heat is something that can raise the temperature of an object.

– The heat to raise the temperature of 1 g of water by 1 C is 1 calorie (cal)

• Energy can be turned into heat: 1 cal = 4.2 J

In the US, for food, dietitians use 1 Cal = 1000cal = 4.2 kJ

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Amount of energy per gram in some common substances

Object or substance Joules/gm Compared to TNT

Type

Lifting a 1 gram object up 1 m (or dropping the same object down 1m)

0.01 or 10-2 0.000004 or 4 x 10-6

Mechanical Kinetic, potential

TNT – the explosive 2,700 or 2.7 x 103 1 Chemical

CCC 20,000 or 2 x 104 8

Gasoline 42,000 or 4.2 x 104 15 Chemical

Uranium- 235 82 Billion or 8.2 x 1010

30 million or 3 x 107

Nuclear

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How does energy turn into work?

• Work is defined as “force x distance”, i.e, lifting an object against gravity, pushing against some opposing force (e.g. a spring) or pressure.

• Typically, energy is turned into heat to increase the temperature of a substance, which expand and perform ‘work’, such as lifting a heavy object or making a motor run.

• One exception is electric motor – it does not work this way. But electricity itself is generated this way, i.e. heating a substance and do work by expansion to generate electricity.

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Why is TNT a dangerous explosive? The concept of power.

• TNT can transfer its energy very quickly:

1 gram of TNT (2,700 J) can turn all that

into heat in 10-6 sec!

• Power is defined as energy/time, 1 W = 1 J/s

• TNT is a ‘high power substance’:

– 2,700J in 10-6 s or 2.7 x 109 w or 2.7 GW (Giga W)

– This 1 gm of material turns into high temperature gas which expands very quickly – explosively.

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Cost of Energy per kWh (USD)

• Practical unit of energy: 1 kWh = 3,600 kJ

Fuel Cost (USD) $/kWh

Coal $40/ton 0.004

Natural gas $3/1000 ft3 0.009

Gasoline $4/gallon 0.1

Electricity $0.1/kWh 0.1

AA Alkaline battery $0.40 ?

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What Duracell says:

AA battery has energy capacity of about 2.5 Amp Hours at Voltage 1.5V or 3.75 watt-hr (1 watt = 1 V-Amp)

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Cost of energy: take home message

• Cost of energy from:

– coal lowest

– Gasoline low but getting higher

– Electricity from power company high

– Electricity from battery Very high

• Since electrical energy is expensive, we should turn off lights when we don’t need them to conserve energy (or to save money.)

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Cost of food energy: high or low?

• Typical daily calorie intake: 2000 Cal , or 2000x4.2 kJ = 8,400 kJ

= (8400/3600) kWh = 2.3 kWh

(Each of us consume energy similar to a 100 W light bulb.)

• Cost of food energy: if you eat in LG5, 80 HKD or 10 USD or about $4.3 /kWh.

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“Energy is conserved” vs. “conserve energy”

“Energy is always conserved”, i.e., energy cannot be created or destroyed; the total amount of energy DOES NOT CHANGE. (First Law of Thermodynamics.)

What then does it mean to say “Conserve Energy” ?

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Conservation of Energy – a fundamental law of science

• The scientific statement that “energy is conserved” does not mean you turn off lights to “conserve energy and save money.”

• If you fire a bullet straight up, the chemical energy in the gun powder became heat and push the bullet up which eventually fell back down into a cup of water, warming the water up. It also left heat in the gun, also some heat in the air due to friction. But if you add all those up, the total energy is exactly that of the chemical energy in the gun powder. This is the scientific meaning of conservation of energy.

• “Energy cannot be created nor destroyed.” If so, why do we need to “conserve energy” by turning lights off?

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Entropy and Energy

• Conservation of energy does not tell the whole story: a hot cup of coffee gets cooler by giving out energy to the surrounding air, BUT, the reverse process does NOT happen.

• Entropy is defined as (amount of energy transferred)/(transfer temperature)

• For something to happen, entropy must increase. (“Second Law of Thermodynamics”)

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Hot things at Thigh can give heat to air at Tlow

• Let’s say energy transferred is 10kJ

• The change of entropy is positive

-10 kJ/Thigh + 10 kJ/Tlow >0 with Thigh > Tlow

• The reverse process cannot happen since the change of entropy would be negative. No go!

• More precisely, the temperature T should be measured in K (Kelvin), with 0 K = - 273 C . Room temperature 27 C is 300 K.

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What is entropy? What is temperature?

• We now know that matter is made out of atoms and molecules – they are very tiny. One mole (18 g) of water contains 6 x 1023 molecules of H2O.

• The temperature T is proportional to the average kinetic energy of each molecule

• The entropy is proportional to the degree of disorder of these molecules.

• It was Einstein who provided the definitive proof that each mole of matter is made of such large number of atoms and molecules by his study of Brownian motion in 1905.

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Laws of Thermodynamics

• The first law: energy is conserved, i.e., the total is constant and never changes

• The second law: entropy will always increase and increase. Equivalently, the universe will go increasingly from order to disorder.

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We do need to conserve (useful) energy

• Useful vs. not useful energy: The minibus from Choi Hung to HKUST requires fuel to run.

After the trip, there is less fuel in the tank. – The first law says that the energy in the fuel used is exactly

equal to the sum of the work done in making the motor run, and the heat exhaust and the energy for the A/C in the minibus etc.

– The second law says that entropy has increased due to this trip, and will NEVER again be at the same level as before the trip.

– The energy in the fuel before the trip is ‘useful energy’ and this same amount of energy after the trip in the exhaust gas etc is not useful, and in this sense, that energy has been ‘used up.’

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How do we use ‘useful energy’?

1. Heat (to cook, to get warm in cold weather …)

2. Mechanical energy (generally by first turning into heat and through expansion to do work). Mechanical energy can be turned into electricity (and vice versa.)

3. Cooling (Very important for places like Hong Kong and Singapore ) .. But how could this be done? Isn’t this forbidden by the Second Law? You will see how!

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Burning fuel (hydrocarbons)

Chain reaction using heat: Start the process with heat to get reaction going, and from the heat generated causes other molecules to react, until all burnt up. Been used for thousands of years for cooking and heating.

Greek scientist Theophrastus (c. 371–287 BC): Among the materials that are dug because they are useful, those known as coals …, and, once set on fire, they burn …

How heat produce motion (mechanical work): Industrial revolution ~1750

• Can all the heat energy be converted to mechanical work?

Efficiency = 100%? The engineers tried and tried and tried

and could never get even close to 50%.

http://www.explainthatstuff.com/steamanimation.html

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Mechanical work does not change entropy

• The Law of Entropy (Second Law) dictates that there is a fundamental limit on efficiency of any heat engine.

• Efficiency (W/QH) is less than

or equal to

1 – (TLow / THigh)

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We need A/C!

How? (Most important invention in 20th century – Lee Kwan Yew 李光耀 )

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‘Cooling by Evaporation’ by Benjamin Franklin, 1758

To John Lining Dear Sir, London, June 17, 1758. In a former letter I mentioned the experiment for cooling bodies by evaporation, and

that I had, by repeatedly wetting the thermometer with common spirits, brought the mercury down five or six degrees. .. We continued this operation, one of us wetting the ball, and another of the company blowing on it with the bellows, to quicken the evaporation, the mercury sinking all the time, ..

During the hot Sunday at Philadelphia, in June 1750, when the thermometer was up at

100 in the shade …one might have expected, that the natural heat of the body 96, added to the heat of the air 100, should jointly have created or produced a much greater degree of heat in the body; but the fact was, that my body never grew so hot as the air that surrounded it… I suppose a dead body would have acquired the temperature of the air, though a living one, by continual sweating, and by the evaporation of that sweat, was kept cold. …May it not be owing to this, that fanning ourselves when warm, does really cool us, though the air is itself warm that we drive with the fan upon our faces; …. that mere blowing of air on a dry body does not cool it, as any one may satisfy himself, by blowing with a bellows on the dry ball of a thermometer; the mercury will not fall; if it moves at all, it rather rises, as being warmed by the friction of the air on its surface …

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Refrigerator and A/C

The coolant is compressed by the compressor (3) and got heated up to a high temperature, gives out heat to the outside air, and enter inside to expand (‘evaporate’) and cool. Electricity powers the compressor.

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Entropy and A/C

• When there is no INPUT of mechanical work, heat can only flow from hot to cold.

• Heat CAN flow from cold to hot when mechanical work is put in, done by the compressor in the A/C unit

• Entropy overall must increase! This is achieved by putting much more heat to the hot source, the outside!

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