The First law of Thermodynamics

Early experimental findings:

we are aware of the experimental observation that both stirring and the application of a burner flame can result in the increase of temperature of a breaker of water. The temperature of the water which goes up as        a result of the transfer of stirring work can be restored to its initial value by a negative heat transfer(or cooling): the magnitude of the negative heat transfer is equal to the heat which can produce the same rise in temperature as the stirring work. Another experiment reported in the literature involves the raising of the  temperature of a given stream of water by a measured amount with an electrical heater which consumes power at a known rate. By such experimental means it was shown that a work transfer of 4.1868 J can raise the temperature of 1g of water by 1°C . The constant of proportionality between work and heat so determined was known as the 'mechanical equivalent of heat'.This is a recognition of the fact that work and heat are quantities of a similar nature. 

We know that mechanical work can be converted to heat by the action of friction , inelastic impact and viscosity. Electric resistance causes the conversion of electrical work to heat. We will soon find that other forms of work can also be converted to heat. The quantitative relationship between work and heat led to the First law of Thermodynamics. 

The first law of Thermodynamics:

Experiments with closed systems which undergo cyclic processes enable us to draw the following conclusion.

When a closed system undergoes a cyclic process , the algebraic sum of the work transfer to it is equal to the algebraic sum of the heat transfer to it.

The above statement is not a logical deduction from other more general and broad propositions regarding the physical world , but no experience has ever contradicted it. Hence it is considered to be a law of nature.This statement , known as the First law of Thermodynamics is one of the bases (singular , basis) of the science of classical Thermodynamics. 

Using our notation that both the work done on the system and the heat supplied to the system are positive , the above can rewritten as ;

dQ + dW = 0 

Perpetual Motion Machine of the First kind (PMM1):

A system which works in a cyclic process and produces a net output of a work (W negative) while having a zero net heat transfer is called a perpetual motion machine of the first kind. We will soon discover that the First law implies that a PMM1 is not possible.

Energy of a system:

There exist a property of a system , called energy(E) such that the change in its value during a process is equal to the difference between the transfers of heat and work.

A Lemma

If Φ is a property of a system , then the change in Φ during a process 1-2 depends only on the states 1 and 2 and not on the nature of the process. Conversely , if there is a magnitude Ψ related to a system such that Ψ changes during a process 1-2 by an amount which depend only on the end states 1 and 2 , then Ψ is a property of the system.

In a cyclic process the net change in a property Φ is zero. Again if we can find a quantity Ψ which shows no net change during a cyclic process then Ψ is a property.

Proof : Let the system under go a cyclic process.(see figure)

If the system follows path 0A1B0 to make a cycle ;

Φ_B dΨ = ₀ ∫¹_~A  dΨ + ₁∫⁰_~B dΨ = 0

If we return to 0 by another path C instead of of B , then ;

Φ_C dΨ = ₀ ∫¹_~A  dΨ + ₁∫⁰_~C dΨ = 0

Hence;

  ₁∫⁰_~B dΨ =   ₁∫⁰_~C dΨ

That is , the change of Ψ during a process does not depend on the details of the process but simply on the end states.
We have quantity E which does not undergo a net change during a cyclic process. By the preceding lemma , E is a property of the system.
Energy is an extensive property ; and it is a consequences of the First law. From the point of view of the First law what interests us is the change in energy of a system and not the absolute value of the energy. In general , the energy E of a system can be expressed as ;

E = U + E_k + E_p + E_s + E_c +E_e + E_m

Where U is internal energy ,  E_k is kinetic energy , E_p is potential energy , E_s is strain energy , E_c is surface energy , E_e is electrical energy , E_m is magnetic energy.
It will be shown later that the energy associated with the molecular structure which can be released by chemical reactions , can be included in the internal energy. Again , let us emphasize that internal energy is not the same as heat. 

The simple system:

When the effects of the gravity , motion , elasticity , electricity , magnetism , surface tension etc. are either absent or insignificant , a thermodynamics system is said to be simple. The energy of a simple system is only in the internal energy mode. System composed of gasses , vapors and liquids fall in to this category. For a simple system , the first law may be stated as ; 

dU = dW + dQ 

or , for a finite process from a state 1 to state 2 , as ;

U₂ – U₁ = W_1-2 + Q_1-2

Internal energy of a system:

Internal energy is the mode of energy associated with the increase in temperature of a system. It is the mode of energy which can be directly affected by heat transfer. However , we shall use the term Internal Energy to signify a particular component of the total Energy , as outlined earlier. Remember that the First law is more than a mere definition of the internal energy by a statement to the effect that it is a thermodynamic property. It states that internal energy is a quantity different in kind from work and heat. Internal energy , being a property , can be said to exist in the system and it can be increased or decreased by a change of state. It is only energy which can truly be said to cross the boundary of a closed system , and the terms work and heat simply refer to two different causes of the flow of energy. In a simple thermodynamic system , the flow of energy which occurs at a result of the movement of a force at the boundary it is termed work , and if it occurs because of a temperature difference between the system and the surrounding it is called heat. The units of Q , W and U are the same in the SI.

It is important to notice that the energy equation concerns changes in internal energy. The First law suggests no way of assigning an absolute value to the internal energy of a system at any given state. For practical purposes , however  , it is possible to adopt some reference state , say 'state 0' , at which the energy , when the system proceeds from this reference state to a series of states 1 , 2 , 3 etc. The internal energy of a closed system remains the same if the system is isolated from its surroundings. A perpetual motion machine of the first kind is thus impossible. ( The perpetual motion machine was originally conceived as a purely mechanical device which , when once set in motion , would continue to run ever. Such a machine would be of no practical value , and we know that , in any case , the presence of friction makes it impossible. What would be of immense value is a machine producing a continuous supply of work without absorbing energy from the surroundings ; such a machine is called a perpetual motion machine of the first kind. The First law implies that a perpetual motion machine of the first kind is impossible.)