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Saturday, November 19, 2016

The car I want to drive

Most major car manufacturers are getting serious about electric cars and most of them are designing cars with all the bells and whistles. I hate to think what they will cost. I believe there is a massive market for a simple, basic, Volkswagen / model T ford / 2cv/Mini - type electric. It wouldn't be for everyone but I believe the market would be huge.

Not only would it be huge in third world countries but also in first world countries. So many of us are fed up with having such a big foot print on the world, fed up with being dependent on someone else to fix our gadgets and fed up with having to tie up a huge proportion of our wealth in a vehicle simply to get from A to B. For other people for whom their very concept of self worth is intimately entwined with driving a fancy car - carry on. Enjoy. The rest of us have a different self image.

Many of us are also a tad suspicious about having every gadget we use being connected to the World Wide Web.  Who wants to be spied on by his toaster (I'm kidding!!!). I suspect we are being spied on by our television sets. (I  am not kidding).  If I want an upgrade to my car, I will pull out, say, a flash drive that goes into a socket in the dash board, take it to my computer and request the upgrade.  Note that many upgrades to ordinary computers smell like idle fiddling by some egg head and often create problems. 

Perhaps I am completely content with the way my car already operates or perhaps I want to wait until some other poor suckers have tested the upgrade before I jump in.  Besides just imagine some bored hacker in his mom's basement hacking some part of the system and bringing a major city to a standstill with gridlock.  Just imagine some foreign power doing the same to your  whole country.  Worse than a nuclear war and leaves the infrastructure intact as they take over.

Of course this also gives Big Brother the ability  not only to follow your every move but to decide to drive your car into a tree or over a cliff at high speed.  You think I am being paranoid.  You have, I assume, being following the revelations of Snowdon and Manning.

I agree most enthusiastically with practically everything Elon Musk is doing and advocating but genius is no guarantee of being right.  Remember a previous genius, Alvin Edison.  He advocated DC (Direct Current) for electrical grids.  Luckily we went with Tesla and used AC.  It is so much more versatile.   Yes, there is a place for DC such as when you transmit power in a cable under water but for the most part, AC is the way to go.

So what would this car be like. It would be both very simple and very sophisticated. Simple in that it would have very few frills, a low selling price and it would be easy for a home mechanic of modest ability to maintain and repair. It would be sophisticated in that it would have the very best engineering and best materials providing reliability, longevity, safety, easy driving, fast charging, recyclability, easy repair and maximum range.

It would be upgradable as new technology became available.  For instance if the new graphene batteries prove to be better than Lithium batteries, when the old batteries finally gave out one could change the batteries to the new sort.  The old batteries would find a new life in private houses to store excess energy generated by your solar panels to avoid sending the power to the grid at knock down prices.  The critical factor is that the new batteries would fit the space where the old batteries lived.

If the engineers insist on producing a hybrid, it would be mostly electrical with a small emergency generator. (a turbine??)   However, consideration should be given to replacing even the emergency generator with more batteries on a weight to weight or volume to volume basis.  So what sort of a car would it be.

The styling would be distinctive.  It would be as recognizable as the  Volks Wagon Combi, Betle, Deux Cheveaux, Model T Ford or Mini.   None of these cars were objects of beauty but they were distinctive.   Clearly it would have to be as aerodynamic as possible and this tends to converge the styling of all cars but there must be no doubt what vehicle you are looking at when you see one of these cars. Easy identification is a big help in making a car iconic. No changes would be made to the styling from year to year. None what so ever. The Beetle didn't need it, neither does our Peoples-Electric.   Not needing to retool for design changes contributes to a lower price.

Driving damage
Bumpers and mud guards should be bolt off and bolt on so that repairing a ding is a simple job of trading in your old part for repair or recycling and bolting on the new part. These easily damaged parts should be compatible for decades. A bumper from the first production model must fit the latest model and vice-versa. Some thought should be given to a hydraulic or pneumatic bumper which could sustain bumps of, say 5 or 10km/h without damage*.

*Nov 2011.  I just read of a jell bumper that a new electric car is using.  Good on you guys.

The Vehicle Manual
The vehicle manual would be straight out of America in their best tradition; the sort of manual that comes out of Time-Life or Readers Digest. They have the most incredible how-to-do manuals where everything is beautifully, clearly laid out and the illustrations are works of art. Once the car had been designed, the wives, secretaries and accountants of the company would be let loose on the car, with the manual, to see if they could change the electric motor, CV joints and anything else that might need to be replaced. If they could not do this, either the manual or the car or both would be redesigned. (No fair changing the secretary or accountant)  A copy of this manual would be standard equipment and would fit in a specially designed compartment in the car.

There would be a standard 'A' tool set and an optional 'B' tool set. The 'A' set would allow one to change a tire and tighten up a screw. The B tool kit would allow most procedures necessary to be done on the car. Very rare tools could be rented from the dealer.  If at all possible the car would be designed to use only conventional tools and to ensure that  a minimum of tools are necessary. The tool kit would fit in a specially built-in compartment in the car.

The Body
Have a think about a carbon fiber reinforced thermoplastic body.  It may not be practical yet but look up the item on YouTube by Amory Lovins in which he shows his audience a half dome of the material and gives them a sledge hammer to see if they can break it.  The car body could go together like pop beads with a smear of epoxy, eliminating all that welding.  The  material is naturally rigid and sound absorbing and able to survive severe crashes while protecting the driver.

The Chassis
Initially there would be only one medium size chassis but eventually there would be three sizes: small, medium and large. On to each of these chassis would bolt the body of a pick up truck (Ute, Bakkie, Tender), a family car, a people mover (van, Combi) or a sports car..... Well maybe not a sports car on the largest chassis but certainly on the medium and small chassis.  Perhaps with modern materials and technology, we might have mono-cock cars with no chassis.

Wrecked or scrapped cars could be taken apart for parts and the parts would fit on any other car no matter what the vintage. Also, in so far as possible, fittings from one size of car would fit on the other sizes. All, for instance, would use the same head light bulb, door handle, radio mounting and so forth.

Yearly Model Changes

This ridiculous system of planned
obsolescence must be made obsolete .

Steering gear
Lets go for simple rack and pinion.  Check out all the cars that used this system and adopt the best one.  Power steering uses power and in a reasonably light car power steering is completely unnecessary.  Besides, Rack and Pinion is cheaper and easy to repair (if it ever needs repairing).  Our Peoples Electric will tend to be a light car with all the frills removed and eventually, as the technology allows, thermoplastic carbon fiber bodies. Rack and Pinion steering will be perfectly adequate.

Nothing wrong with wind up windows but make them of quality material so that they wind up smoothly when you buy the car and just a smoothly in 20 years.  Remember, no planned obsolescence.  Electric windows use power and are more expensive to build and repair than mechanical windows.   

OK you can have your electric windows if you insist but that is a far as I am prepared to compromise my people's electric.

Car Magazine
A quarterly car magazine would give interesting hints on how to maintain your car, maps of places to exchange or charge your batteries and quirky stories of how someone had crossed the Sahara with the car fitted with solar panels and how someone else had fitted a chuck wagon stern to his vehicle and gone on roundup.  It would be interesting, informative amusing and iconic. It could be delivered to your reading device or in a paper form if you prefer.  Some of us Luddites like paper.

Solar cells
Solar cells must eventually be fitted on every possible surface.  The technology is probably not there yet but is advancing rapidly.  Very interesting work is being done on allowing all panels to contribute their full generation capacity despite a lack of co-linearity and despite some panels being partially shaded. When we have power point tracking for individual solar cells, these technologies will greatly increase the effectiveness of the solar cells which clad the car. At one time solar panels were stiff and flat.  Now one can buy flexible panels.  It should soon be possible to clad any shape and get the full power from each cell.  In addition there is work on producing power from windows.

 Note that the solar panel retrofit on the Prius on the roof between the front and rear window is reputed to give about 10 km extra for a day in the sun. A nice little bonus. With advances in the technology and panels on the whole car, one might get, say, 25 extra km per sun-day*. We're not talking here about a completely solar car.  Just a nice little bonus for a day in the sun and the possibility of getting home if you forgot to charge and ran out of gas (sorry - electricity)

*Note that since the writing of this article there has been an item in the news (The NZ Press, feb 2010) that IBM has developed a solar panel using only "easy to find" minerals. If this development becomes commercial, the cost of solar panels should plummet even further. They already are on a toboggan ride.  Standard panels coming out of China are already (2012) down to a dollar per nominal watt.

Mechanical Design
The designers would endeavor to use the most commonly available parts much like the Skunk Works does. The Skunk Works only innovates parts that are necessary for the special functioning of the aircraft in question. The rest is off the shelf. If a certain tire rim with a certain spacing of stud is the most common in other cars of the world, this size should be adopted. If a certain head-light bulb socket is most common all over the world, this one would be used and so forth. This would ensure that if you were stuck, you would have a good chance of finding parts that would get you by. Conversely, scrapped cars of this type would be a rich source of parts, even for other makes. Even better for the company, people with other types of vehicles would always try to buy from the company because of the high quality and competitive pricing of their parts.  Having your parts fit other cars would ensure a large market.

None, Nada, Zilch. This may sound revolutionary..... and at first, not having a warranty would be a negative selling point. At the very least, make it an optional extra.  As confidence builds up in the reliability of the car, people will relax about the lack of warranty. In fact, a lack of warranty will quickly become a major selling advantage. 

Warranties cost the company money and this is built into the price of their vehicles. The savings from the lack of warranty must be passed on to the customer. An added effect would be that people would not thrash their car during the warranty period. They would look after their cars from the start.

Besides, as mentioned above, the cars would be so easy to repair that any joker with a basic set of tools and the manual could repair any part of the car. By their nature, electric cars will be far simpler than petrol cars.  Moreover computer boards are simply unplugged and reprogrammed or a new one plugged in.  Computer chips are as cheap as,,,,, well chips, and software when spread over many users is also cheap.

Dealers would locate in the low rental industrial areas of cities or towns. Only one dealer would be allowed per city or town. In their warehouses they would sell the cars and have a full stock of spares. They would never ever ever ever run out of spares. Their computer system would flag when they had to order parts to keep their inventory up to date. A dealer who couldn't do this would loose his dealership. All dealers and their staff would be sent to the factory to practice doing everything on the car that could be done but they would not be required to do repairs at their dealership. They would be there to provide advice and parts.

Undoubtedly, there will be  computer chips in the car. How about using one of those computer memory sticks (flash drives) that people use to transfer information from computer to computer. Have it plug in to the dash board. Taking it out and plugging it into your PC would run a diagnostic and you could reprogram the chip for maximum efficiency or maximum performance or for whatever other options were available right from your PC.  Hardware is expensive.  Software, when spread over many units is cheap.

The Battery
This is out of the hands of the company but every effort should be made to standardize batteries between different makes and models of cars. For instance, the battery of a Tesla should fit a Volt and vice versa. It would be well worth while looking at the Project Better Place option.  At the very least, a new company developing an electric car could adopt the battery design of other cars right from the outset and build the car around that design.

Apparently the lithium ion battery is now obsolete and the Lithium titanate, lithium iron phosphate and lithium polymer batteries are far longer lasting.  The polymer battery, is apparently much lighter.

Graphene batteries are on the horizon with the discovery that with an addition of water, the layers of grapene do not fuse.   Batteries can be upgraded as technology allows but can still have the same outer aspect so that they can be used in older vehicles. The batteries might be based on a standard cell of 2x3x5 cm that could be combined in series and parallel to achieve whatever voltage the particular car uses and combined in different physical configurations to fit virtually any available space.  Incidentally, such batteries would find uses in a wide variety of other applications including power storage for the home.  There would be a huge market for both new batteries and batteries which no longer had the capacity to be used in a vehicle.

All components of the car must be designed to be completely recyclable. All parts will have a core charge just as is done with glass bottles and given back when the part is returned. This would ensure that worn out cars would not litter the environment. People who are too rich or too lazy to recycle their vehicles would find any number of people who would take the vehicles off their hands to recycle parts or to get the return fee.

A great beauty of electric cars is not only that you save on fuel but also on lubricants. An electric car can be built today that needs no lubricant except perhaps a little 3 in 1 oil for the door hinges. Remember all the grease points we used to have to attend to at each service. These don't exist on modern cars.  Electric cars do not have an oil sump.  More saving of our too-valuable-to-burn fossil fuels.

Electric motors are so reliable that one could have a car quite soon that would last almost a lifetime. You would probably change the upholstery 4 or 5 times before the car wore out. Israel is about to convert to electric cars provided by Renault-Nissan with reticulation and battery exchange provided by Project Better Place. If successful, this will cause a paradigm shift in the car market. A very attractive option is to for a new car builder to build a car with a battery that can be changed by Project Better Place stations*.

 *It appears that the Project Better Place company has been bought and shelved.  This smacks of interference by the oil or conventional car companies.  They are fighting a rear guard action and will loose in the end.

The world is ready for a simple affordable car. Renault is now building the Logan which already goes some way towards a "peoples car" and demand has outstripped anything the company expected. Of course it is a petrol car but they have tapped a market that they didn't know existed. Renault has been absolutely amazed by the response of the public in France. Tata in India has done the same. Obviously a simple car is not for everyone but all over the world there is a longing for simplicity, for having a smaller footprint on the world and for being able to look after yourself rather than having to depend on a specialist for all your needs. If Renault "keeps the faith" and isn't tempted to slowly turn the Logan into a conventional car, it will sweep the world. By the time other manufacturers wake up and smell the flowers, the Logan should have captured the imagination of the world and a huge chunk of its markets. How much more would a simple electric car capture our imagination.

Self Driving
No no no!  I don't want a car that drives itself.  I like driving.  I certainly don't want my car connected to the world wide web.  Have you any idea the vulnerabilities we are exposing ourselves to by putting all our activities into the hands of 'big brother'.  How exposed we are to being hacked, not only by some 14 year old kid in his mom's basement but by government agencies.  Give me a simple but well engineered car and if possible one that I can maintain myself.  Make it highly recyclable.  If as many scientists predict, we are heading for a collapse of our civilizations which will put us back at least into the dark ages, any idea how valuable an electric car will be, after the crash, that you charge at your own solar panels on your roof and that doesn't depend on a www that has collapsed.

And finally
If a car manufacturer does this, eventually it will have to down-size. Such a car will saturate even the world market and The Company will then be providing top up cars and parts. And ultimately, isn't this what we want: a much smaller car manufacturing sector, using less raw materials and energy and producing usable, long lasting cars for the public. We are just on the brink of an ecological melt down and must reduce our foot print on the world. We don't all want to be living the way the kids were in the winner of this year's (2009)Oscars*.

*Slum Dog Millionaire

What is certain is that the car manufacturer that twigs on to this philosophy first will capture a huge share of the market.  If this car comes from America, the world is their market.  If it comes from some other country, America and the rest of the world is their market.

Saturday, November 5, 2016

Some basic science

If you want to  to make sense of the weather, the climate and climate change, at the very least you need some basic science.  As our education curriculum gets more and more crowded by IT and other subjects, many of these concepts are not being taught and they are interesting.  Way back, when I was in High School, the basics were taught and became part of our core knowledge.  (Sorry to sound like an old fart but I guess I am)  So hear goes.  No particular order.  I will type them as I think of them.

Sensible Heat (as in 'to sense something' - not that the heat is somehow morally superior to some other unsensible type of heat)

This is the heat that it takes to raise the temperature of something or the heat that must be removed to cool something.  The small calorie (with a small 'c') was defined as the amount of heat needed to raise one gram of water by one degree centigrade.   There is also a large Calorie (with a capital 'C') which is the amount of heat to raise a kilogram of water by one degree.  Clearly since there are 1000 grams in a kilogram, there are 1000small calories in one large Calorie. Incidentally, if you need to work in SI units, One calorie (small 'c') is equal to 4.1813 joules*.

*A Joule is one watt second.  In other words a watt (of electricity) acting for one second.  If a one watt heater was immersed in a gram of water and operated for 4.183 seconds, it would heat the water (assuming no heat loss) by one degree C (or K if you like).

Latent Heat 
I defined sensible heat first in order to make it easier to define Latent heat.
Latent heat  is the amount of heat needed to melt or evaporate a substance or conversely, the heat that must be removed to condense or freeze something.  
This is a core concept when talking about weather and for a whole range of other subjects.  I'll use the old calorie units here because it makes the explanation easier. 

When you melt ice, it takes a lot of heat. Specifically 80cal (334j) per gram.  This is the same amount of heat that would be needed to raise a gram of water from 0 degrees   to 80 degrees C.  Conversely, when water freezes, each gram gives out 80 calories.  Some people ask; "so if heat is given out, doesn't that warm the water".  No, but to a good first approximation, it keeps the water at zero degrees until all the water is frozen.  Similarly, when you boil water, it stays at 100 degrees while the water is being boiled off.

The energy needed to change  liquid water to water vapor is even greater.  To evaporate one gram of water takes 532 cal (2264j) or enough heat to raise a gram of water from 0 degrees C to boiling 5 times over and then a bit.  Of course, when water vapor condenses into a liquid this same 532cal is given out.

Since we have these two, we can add them and find the heat of sublimation.  This is the heat needed to change solid ice to a vapor directly without going through the liquid phase.  This is 532+80 =  612cal (2598j) per gram of ice.

As an interesting corollary* of this: if moist air blows across ice and the cooling of the air by the ice causes the water vapor to condense out as water, every kg of water condensed out of the air will melt 532/80 = 6.65 litres of water from the ice.  Think of a moist foen wind blowing across Greenland for instance.

*A corollary is something that results directly from some previous fact(s).  Usually used in Math.

If you look at the table in the link above, you will note that two substances, Ammonia and Water have much greater phase change energies (latent heat) than other substances in the table.  The reason is of interest.

You have probably heard of the experiment of Earnest Rutherford who worked out that atoms are not like plumb puddings but more like solar systems.  Most of the mass is concentrated in the center and most of the rest of the atom is empty space.  The solar model was an improvement as far as it went but later it was worked out that while the so called 's' sub orbits were pretty well circular, the 'p' sub-orbitals were dumb bell shaped.     In water, the hydrogen attaches to the ends of two of these dumb bell sub orbits making the water molecule an angular shape.  Move your thumb and index finger as far apart as you can and look at them.  The Oxygen atom is located where your thumb and fore finger join and the hydrogen atoms are on the ends of the finger and thumb.

The electrons spend much of their time around the oxygen atom leaving a naked proton at the other "end" of the molecule.  Not only is the water molecule charged (positive at the Hydrogen side and negative at the Oxygen side) but there are no electron orbits closer to the hydrogen nucleus to keep other molecules away.  A negative charge can get much closer to the Hydrogen end than with other atoms and hence the bond is stronger*.  This is the famous Hydrogen bond.

*In general, a force field decreases with the square of the distance from the object creating that field. 

This is the explanation why it takes so much energy to melt or evaporate H2O.  The water molecules, because they have a positive and a negative side, cling together.  This is also why their melting and vaporization temperatures are so high compared to other molecules of a similar molecular weight.

Incidentally, if you want to visualize ammonia, spread your first two fingers and your thumb far apart.  The Nitrogen atom is where they all meet with the three Hydrogen atoms on the ends of your fingers and thumb.  Just like water, ammonia has a positive and a negative end (side) and the positive ends are naked hydrogen atoms (protons) and hence form the famous hydrogen bond.

You might wonder how a molecule of water can leave the surface of the water and go into the air. After all, it is at the temperature of the water and the molecules cling together.  It is a little like a rocket leaving the earth.  It has to have enough energy to break free of gravity.  The water molecule has to have enough energy to break free of the electrostatic attraction to other water molecules. The answer is that temperature is a measure of the average energy of the molecules As they bounce off each other, as long as energy is not being added or removed from the body of water, the average energy stays the same.  However this is only an average.  As they randomly bounce off each other, there will be some that have more velocity and some less.  Some molecules on the surface will have enough energy to rocket into the air.

Incidentally, this is the explanation why evaporating water cools the surface it is on.  The energetic (hot) molecules leave, leaving behind the less energetic (cooler) molecules.  They absorb heat from the surface they are on and in turn some of the energetic ones rocket into the air.

Avogadro's Number
Some genius worked out that a given volume of any gas at the same temperature and pressure contains the same number of molecules. (it wasn't Avogadro)  Oxygen exists in the air as a molecule of two oxygens joined together as does hydrogen and nitrogen.  This is rather convenient since if you know the molecular weight of any gaseous molecule, you know it's relative specific gravity (how heavy it is compared to other gases).

Hence, Oxygen has an atomic weight of 16 (rounded up), it's molecule is 32.  Nitrogen is 14 so its molecular weight is 28 and water is 16 plus 2 equals 18.  Air (very approximately) has a molecular weight of 30 (between Oxygen and Nitrogen*).  Water vapor therefore has a density of 18/30 = 3/5th or 60% of air.  Counter to what might think, a mix of air and water vapor (humid air) is  lighter than dry air.

* I haven't taken into account that 4/5th of air is N and 1/5 is oxygen or the actual mollecular weight of the gasses.  This would alter the calculation slightly.  The above is what one calls a first approximation.

Note here that when you dissolve sugar or salt into water, the solute (solid) to some extent fits between the water molecules so the volume of the resulting solution is less than the volume of the original water plus the volume of the original solute.  With gas this is not so.  If you add a gas to an existing gas, it increases the volume by exactly the amount that you added.

Ignoring the Fahrenheit system that only a few primitive societies still use, the centigrade system is as follows. (conceptually - there are a few minor whichevers and we will have a look at them later).

Using a thermometer, you mix ice and water and note where the liquid in the thermometer settles down.  You make a mark and call this 0 degrees Centigrade.  You then boil the water and once more make a mark where the liquid comes to in the shaft of the thermometer.  You call this 100 degrees Centigrade.  You divide the difference into 100 gradations.

Absolute Temperature
Using the same gradations you go downward until you can't remove any more heat from whatever substance you are examining.  You find that as low as you can go is about 273 degrees below the freezing point of ice.  This is called absolute zero and is a point at which no more heat is held in the substance. In Kelvin,(the absolute system)  the freezing point of water then becomes 273K and the boiling point of water 373K

A way of getting a first estimate of absolute temperature is to cool a gas and note its volume as you hold the pressure constant.  Draw a graph.  Where the volume goes to zero is a good first approximation of absolute zero.

How about the whichevers.  First then a word on isotopes.

The nucleus of atoms contains positively charged protons and no charge neutrons.  The neutrons, somehow hold the protons together from flying apart. Don't ask me how.  That is above my pay grade. The protons are all positively charged and you might remember from science that same charges repel each other.  In any atom, there are approximately the same number of neutrons and protons.  This is not quite correct and becomes a little less so for the heavier atoms but it is a fair first approximation.  A given element, let's say Carbon, always has six protons.  This is why it is carbon or to be more accurate, it has the same number of electrons as protons and 6 electrons results in the physical and chemical properties that we know as carbon.

However, within limits, it can have various numbers of neutrons.  Carbon can have 6, 7 or 8 neutrons and hence Carbon 12, Carbon 13 and Carbon 14.  Carbon 12 and 13 are stable but Carbon 14 is not.  If you have an atom of Carbon 14 it will at some point fly apart.  You can't know when this will happen for any given atom but it has been observed that with large quantities, you know how much of the carbon 14 will break down in any period.  It turns out that half will break down in 5730 years and half of the remaining half in another 5730 years and half of the remaining quarter in another 5730 years.  This makes it very useful for dating organic material and I will explain this later and give you the math needed to date objects.  It is not difficult.

You might wonder why there is not an equal amount of Carbon 12 as 13 if both are stable.  I don't know.  Carbon 12 is far more prevalent.  Perhaps for some reason more Carbon 12 is produced in super novas that carbon 13.  If someone knows, put a note on the bottom of this  blog.  

Most elements have a number of isotopes and some are stable and some are not.  The unstable ones have half lives which vary in the different elements from miliseconds to millions and millions of years.  It is not always the heavier that is the most unstable.  For instance Uranium 235 is less stable than U238. Apparently certain configurations are in a sweet spot.  The search carries on to find trans-uranic elements which have sweet spots.

So back to Temperature
Water can be made from any of the isotopes of Hydrogen and Oxygen. Hydrogen has three isotopes, namely ordinary hydrogen with one proton in the nucleus, Deuterium with one proton and one neutron in the nucleus and, you guessed it, Tritium with one proton and two neutrons.

Oxygen has three isotopes, O16, 17 and 18.  Since she has 8 protons, these isotopes have 8, 9 and 10 neutrons in the nucleus.  In this case, O16 is the stable one. (often although not always, the lighter one is the stable one.) So what does this mean.

If the lightest Hydrogens reacted with the lightest Oxygen, you would have a molecule with 18 nucleons.  This is as light as water can get.  If the heaviest of both linked up you could have a water molecule with 24 nucleons.  Since virtually all the weight of an atom is due to the nucleons, you can have a wide range of weights.  Say for a first approximation that all the atoms in the water you are using to establish your thermometer have the same energy.  To have the same energy, the lighter molecules are moving faster. (energy is equal to half the mass times the velocity squared) so they will more likely have escape velocity if they find themselves at the surface of the water.  So what happens.

The light molecules fly off preferentially leaving the heavier molecules and as you continue to boil the water, the temperature rises.  The reverse is also true. The heavier molecules of water condense more easily (at a higher temperature) than the lighter ones.

This, of course, makes the calibration of a thermometer a tad difficult as the boiling point of water (if you want to be picky and scientists are very picky) keeps changing as you boil it.  Of added difficulty, some sources of water have slightly different proportions of isotopes than others.  

Boyls Laws
These are pretty simple and also come from observation.   Simply stated they are as follows.

If you increase the pressure on a volume of gas, the volume decreases.  If you double the pressure you half the volume.  Nature could have given us some other relationship between pressure and volume.  Isn't it nice that it is such a simple relationship.

If you heat up a gas, its volume increases.  Here though, we are talking about absolute temperature.  If you double the absolute temperature, you double the volume. (if the pressure is kept constant). Again, nice that nature provides such a simple relationship.

For instance if you were to raise the temperature of a gas from the freezing point of water to the boiling point of water you would increase its volume by 373/273 or by about 1.366 times.  (that is why I told you about absolute temperature first).

The earth is about 25000 miles around its equator.  It rotates on its axis once a day.   Hence if you are standing on the equator you are traveling at about 1000miles per hour eastward.  If you were standing on one of the poles, you would rotate once per day but are moving at 0 miles per hour (we are in an earth reference frame).  Of course the earth is moving through space and you with it but that is neither here or there for this example).  If you fire a cannon ball northward from the equator in the northern hemisphere, In addition to its northward velocity, it is traveling sideways toward the East at 1000mph.  It will still be traveling toward the East as it flies through the air but the ground over which it flies is traveling slower and slower, the further north you go.  Looked at from above, the object veers to the right in relationship to the earth below.  As you can see, the effect is greater, the further north you go.  If you go from the equator to a degree north of the equator, the sideways velocity hardly changes.  If you go from one degree south of the North Pole to the North Pole, the change in velocity is large.  The same occurs when you move something southward in the Northern Hemisphere.  It veers to the right.  This effect has some profound implications on our weather.

Radioactive dating
As I mentioned, radioactive isotopes break down into simpler atoms.  Certain proportions of protons and neutrons in the nucleus are not stable.  It was observed fairly early on that if you measure the time it takes for half of the radioactive isotope to break down, then half of the remaining will break down in the same time, half of what remains in the same time and so forth.  This is called the half life.  I'll use Carbon as the example since it is valuable for the dating of organic material. Carbon 14 has a half life of 5730 years.  You might ask, if it has a half life so short in comparison with the age of the earth, how come there is any of it around now.  Also, you would have to know how much was in a living organism when it died in order to measure how much there is now and use these two figures to date it.  The answer is rather neat.

Carbon 14 is continually being produced in the upper atmosphere by an atomic reaction.  When high energy cosmic rays hit Nitrogen 14, some of it is converted into Carbon 14.  To a first approximation (more of this later) its rate of production has been constant over time.  Living organisms incorporate carbon into their bodies throughout their lives but when they die, no more is taken in.  The Carbon clock starts and if you can measure the proportion of Carbon 14 in relation to "ordinary" carbon, you can tell the age of the artifact.  Now for the math. Co is the amount of carbon in the artifact (piece of wood) at time zero.  That is to say, when the wood died and stopped taking up carbon.  Ct is the amount of carbon at time 't'.  That is to say when you took the artifact and decided to measure it.  1/2 is just what it says.  One half.  and 'n' is the number of half lives that have gone by so we have the formula.

Ct=C0 X (1/2)n. Also written in algebra without the times sign as Ct=Co(1/2)n

Lets look at this.  Suppose you start with 8 grams of a radioactive element and one half life has gone by.  You raise 1/2 to the first power which leaves it as 1/2 and multiply by 8.  Answer 4 grams.  Suppose two half lives have gone by.  You raise 1/2 to the second power (multiply 1/2 by 1/2) and you get one quarter.  Multiply this times 8 grams and you have two grams.  Let's do one more.  Three half lives have gone by.  You raise 1/2 to the third power (multiply 1/2 times 1/2 times 1/2) to get 1/8.  Multiply 1/8 times 8 and you get one gram.  So this formula works.  Now let's make it a little more sophisticated.  We will define 't' as the time that has gone by and 'h' as the half life of the isotope we are working on.

Clearly the number of half lives that have gone by equals t/h. Say the half life of an isotope is 10 years and 30 years have gone by.  Clearly three half lives have gone by.  In other words n = 30/10.   We can now substitute this into our first formula.  Where we had n we will put t/h so Ct = C0 x 1/2(t/h).  

 Now we have the formula in what I call the forward or straight forward form. In other words in the form that is easily understood, we can now "solve for" any of the terms. In other words make t or n or Co the subject of the formula. If you remember your algebra, since the right side is equal to the left side, as long as I do exactly the same to both sides, the formula will still be valid. I could multiply both sides by some number, square or take the square root of both sides and so forth.   The trick, of course,  is to choose the correct thing to do to both sides to get the term I want as the subject of the formula.  Why bother. Well, sometimes I might want to work out the age of the artifact 't' or the half life of an isotope 'h' so it is useful to change the formula around to make the desired factor the subject of the formula.  Of course to work out 't' or 'h' I would have to know the value of the other terms in the equation.

Let's solve for 't', the time that has gone by.  Then we will have a formula we can use for dating an artifact.

I start with the formula Ct = Co x (1/2)t/h

I divide both sides by Co resulting in

Ct/Co = 1/2(t/h)

Now you will have to take my word that the following identity is correct.  To explain logs at this point would take a tad too long.

logABC (log to the base A of B to the Cth power) = C x logAB (C times log to the base A of B).  In other words, you can put the exponent before the log and the value remains the same.   So first we will take the log of both sides.  You don't have to understand logarithms but only the principle that if we do the same to both sides of an equation, the formula is still correct.

Log10(Ct/Co) = log101/2(t/h) 

Using the conversion (moving the exponent, (t/h) in front of the term on the right side, I get:

Log10 (Ct/Co) = (t/h) log10(1/2)

Now to get t by itself, I simply divide both sides by (log10((1/2)) and multiply both sides by h to get: t=hlog10(Ct/Co) / log101/2

I said that this was a first approximation.  It was seen that the value obtained for objects of known age differed slightly from the theoretical value.  For instance, in the high mountains of America is a species of tree known as the Bristle Cone Pine. As with many trees it has growth rings and live trees have been found that are 5000 years old.  In addition, in the area, there is dead wood which with Dendrochronology can take the age back another 5000 years.  Carefully shaving off individual growth rings and carbon dating them showed a small variance from the theoretical value.

The best explanation for this is that the rate of C14 production has not been exactly the same over time.  Cosmic rays come from violent events in the universe and have varied over time.  What is good, though, is with the application of this correction, the age of artifacts of known age slotted into place.