XVI(B) Everything in the universe is made of math----.including you and I.u

XVI(B) Everything in the universe is made of math---including you and I
[Contd. A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri.]
      A tale of how we have tamed the Fire Demon and turned him to be a Good Samaritan for us to serve us at our beck and call.
          

As Scientists and evolutionists believe that learning to make and control use of fire was likely one of the earliest discoveries made by pre-humans who walked upright on two legs. They used fire for multiple purposes: to get light, heat to cook plant-products and animals, heat-treatment of stones for making tools, to keep predator animals away, to burn clay for ceramic objects, to light camp fire as beacons for those away from camps etc.

Fire delights us, mystifies us and sometimes terrifies us when fire sparks and catches to property and wealth causing extensive damage or destruction and even rendering our lives at stake. From ancient times many people fear fire so much that they worship it.

Thousands and thousands of years have passed since our distant ancestors could make use of fire in their practical lives; but they did not know the real characteristics of fire. We have travelled a lot and invented a powerful tool, “Science” by which we come to know that fire is a chemical reaction of oxygen and a fuel source and is a most common means of transferring chemical energy to heat energy. It is a natural reaction that fire didn’t to be invented. When lightning strike a forest, it might have created fire which was definitely witnessed by earliest creatures predated human beings and it probably intrigued and amazed them.

The actual breakthrough in the realm of fire, so to speak, came in 1798 when Sir Benjamin Franklin, Count Rumford (1763-1814) an America born British military engineer propounded that heat is a form of energy and paved the way for the birth of physics dealing with heat based on mathematical formulation and equations called “thermodynamics”. Another pioneer in this field was Sadi Carnot (1796-1832), a young French military engineer who attempted to find a mathematical expression for work produced by one kilogram of steam and eventually introduced the concept of heat engine. These ideas were further developed mathematically by Rudolf Clausius (1822-1888), a German mathematician and physicist into the First and Second laws of thermodynamics. He is credited with making thermodynamics a Science.

Let us see another very interesting aspect of heat against the backdrop of this vast universe. Present day cosmologists, astrophysicists and scientists narrated a fascinating story about the birth of this universe. Based on experimental observations and applying highest mathematical skill they convinced to believe that about 13.8 billion years ago, this observable universe was quizzed into a tiny particle under tremendous gravitational pressure as an embryo in a cosmic egg. All on a sudden a colossal explosion occurred, which is now famously known a “Big Bang”, releasing stupendous heat. Thereafter, all other energies, matters known to us now and so far mysterious dark energy, dark matter were born out of that initial energy of the universe, namely, heat.

In this process, our Earth was born as a planet of the star, the Sun, about 4.5 billion years ago.

Evolutionist believe that life sprouted on Earth in lifeless material particle about 3.5 billion years ago and our pre-human ancestors have been around Six million years while the modern form of humans evolved only about 200,000years ago. So, how important is heat behind our life and for our life! It is not known exactly when our distant ancestors tamed fire (heat) and applied it for practical uses. Armed with the remains of Africa, Asia and Europe some researchers claim that controlled use of fire started as early as 1.5 million years from now.

Still we are using it for our various needs of everyday life but not in the same way as our distant forefathers did. Equipped with the knowledge of the laws of thermodynamics* we have mastered the technical skill to utilize heat scientifically and mathematically in the most elegant way to serve various purposes of modern life.

Thermodynamics has several types of applications in our daily life, though most of us are not fully aware of it. It is used in thermal power plants, spark engines like cars, motorcycles or any other two-wheeler fueled by petroleum, trucks, in ships, in aeroplanes and many other engines work on the principle of thermodynamics (more specifically on the basis of second law of thermodynamics). They may be using petrol or diesel or any other fossil oil but the principle remains the same.

Cooling machines, such as refrigerators and conditioners actually use heat, simply reverting the usual process by which particles are heated. The refrigerator pulls heat from its inner compartment, the area where food and other perishables are stored and transfer it to the region outside. This is why the back of a refrigerator is warm. All refrigerators, deep freezers, industrial refrigeration systems, all types of air-conditioning systems, heat pumps etc. work on the principle of thermodynamics (here also, on the basis of second law of thermodynamics.)

One of the important fields of thermodynamics is heat transfer, which relates to transfer of heat between two media. There are three modes of heat transfer --- conduction, convection and radiation. The concept of heat transfer is used in wide range of devices like heat exchangers, evaporators, condensers, radiators, coolers, heaters etc.

So, heat, so to say, thermodynamics is playing important role in our everyday life and made it cosy. But math has played an inherent, important role behind it.
        [*What are those Laws of Thermodynamics which are so useful to us today?Initially there were three laws of Thermodynamics:First law,Second law and Third law.
First Law:"The total amount of energy in an isolated system is conserved"
That means,energy can neither be created nor be destroyed.It can only be changed from one form to another and hence the total energy of this vast universe will always remain the same.This is actually the golden rule of "Conservation of Energy" in the world of science.The most interesting and baffling fact is that the total energy of this universe is zero and will remain zero for ever(curiously enough there are equal amount of positive as well as negative energy in this universe.) From this law we also get a quantitative relation of work done by heat supplied to a system.Which is:For a thermodynamic cycle the net heat supplied to the system equals the net work done by the system.This first law of thermodynamics was propounded by Rudolf Clausius in 1850.
 Second Law:"The entropy of the universe tends to a maximum."
To get some idea of this law,at least in a nutshell,we must  know what is meant by "entropy". But it is not easy to fathom its meaning for ordinary people like us.Yet to get a crude idea it may be said: Entropy of an object is a measure of amount of energy which is unavailable to do work.Entropy may also be regarded as a measure of uncertainty or randomness.
From the second law of thermodynamics we get the idea that :whole amount of internal energy of any substance is not convertible into useful work. One portion of this energy which is spent for doing useful work while the remaining part, called unavailable energy, can not be utilised for doing work.The measure of this unavailable energy(per unit temperature) is termed 'entropy'.
  Examples of increase in entropy in our everyday life:When a gas expands in a vacuum,water flows out of a reservoir,a body is heated or cooled  etc.So where there is a transition from an ordered state to less ordered state of affairs there is an increase in entropy.
Around 1850 Rudolf Clausius and William Thomson stated both the First Law and Second Law of Thermodynamics.
Core idea of the Second Law of Thermodynamics:Heat does not spontaneously flow from colder to a hotter body.
Everything cools to its surroundings-----a hot car engine,a cup of hot tea,a red-hot iron rod cools to room temperature.It does not get hotter unless it get energy.
 Third Law:"As the temperature of a system approaches absolute zero
(−273.15°C, 0 K),then the value of entropy approaches a minimum"
The third law of thermodynamics gives us an idea of what will happen when the temperature of a substance approaches Absolute Zero.But what is Absolute Zero temperature? In 1800s scientists tried to find a relation between volume and temperature of a gas and theorised that volume of a gas should become zero at a temperature of -273.15 degree Celcius.In1848 William Thomson(best known as Lord Kelvin) took this temperature as Absolute Zero which is denoted by 0 K to remember him.Theoretically  absolute zero is the lowest possible temperature in this universe but not attainable practically.The coldest temperature  we could measure is3K,not on Earth but in the distant depth of the universe,beyond stars and galaxies.Yet this law has many important applications.
The third law was developed by a German chemist Walther Nernst during the years 1906-1912.
                 Much later after those thee laws were established ,scientists realised that another law was needed to incorporate formal definition of temperature and logically it should supersede those former three laws.Ralph H. Fowler propounded this law in 1935 and rightly placed it on the  top of those three laws and named "Zeroth Law of Thermodynamics".
                It states:"If two thermodynamic systems are each in thermal equilibrium with a third,then they are in thermal equilibrium with each other"
               In essence it tells that if  temperatures of two bodies are the same with a third body then they are said to be all in thermal equilibrium and there will be no flow of heat from one into the other when they are put in contact with each other.It seems very obvious but incredibly important to establish that temperature is a fundamental and measurable property of a matter.This is the basis for construction of thermometers which we need to make thermodynamics a quantitative science.]

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