First Law Of Thermodynamic: The Concept Of Energy Conservation

First of all we will learn about thermodynamics, what is thermodynamics? 
........."Thermodynamics is the science that deals with the relationship between heat and other forms of energy. In particular, it tells us that how thermal energy is converted into other forms of energy"............
We saw the zero law of thermodynamics and its statement in our previous post. Now in this post we will learn about the First law of thermodynamics and their statement. 

First law of thermodynamics was developed empirically over about half a century. The first full statements of the law came in 1850 from Rudolf Clausius and William Rankine. Rankine's statement was perhaps not quite as clear and distinct as was Clausius. Why they proposed it most probably because no one has done that yet!!! Afterall this law was nothing but a thermodynamical way of expressing law of conservation of energy…..
........"The first law establishes the relationship between Heat, Work and Internal energy".......

Before trying to understand the first law of thermodynamics, we need to understand about a term called as “Internal Energy”. The term internal energy came into existence as a consequence of the first law. 
It is defined as, "The energy stored in the system by virtue of configuration & motion of the molecules constituting the system is called it's Internal Energy". It is a definite property of the system & denoted by 'U'.

There are small atoms in all the substances which possess various types of motion. These motion can be;
(1) Rotational motion
(2) Vibrational motion
(3) Translational motion
Thus;
........!!Internal Energy Is Just The Sum Of All These Possible Energies Inside The System. Change In Internal Energy Refers To The Change In The Total Energy Of The System!!!!.......


The First Law Of Thermodynamics
The first law of thermodynamics is an extension of the "Law Of Conservation Of Energy". That's why we call the first law of thermodynamics the law of conservation of energy. This law states that, "Energy can neither be created nor destroyed. Since there are many forms of energy therefore it can only be transferred from one form to another within an isolated system". 

.......!!!The Two Forms Of Energy Interections Considered In The First Law Of Thermodynamics Are Heat And Work!!!.......
Thus, the first law of thermodynamics deals with the energy of a system (typically, internal energy) and its interaction with its surroundings across the boundary in the form of heat and work transfer.
For Examples
(a) In your home appliance like fan, mixer, grinder, etc, the electrical energy is converted into mechanical energy. Here also the energy is transformed from one form to another.
(b) Consider a hot coffee on the table, after some time we see that the coffee becomes cold(relatively) this is due to the heat dissipation from the coffee to the room..
(c) Water flows over a dam to generate electricity by converting potential and kinetic energy into electrical energy.

General Statement Of First Law Of Thermodynamics
The first law of thermodynamics states that,
........."The total energy of an isolated system or the universe (sum of system and surrounding) is constant or remains the same. Though it may be exchanged between system and surrounding. But It neither increases nor decreases"...........
EXPLANATION 
In thermodynamics, we deal with systems and surroundings (or with two separate systems). Whenever there is an energy change between the system and its surroundings, it is assumed that the entire energy of the system and its surroundings is conserved (or remains constant). Because if energy is lost by the system, it gets absorbed by the surroundings. And if energy is absorbed into a system, that energy is released by the surroundings. Thus, the total energy remains conserved.

Mathematical Form Of First Law Of Thermodynamics
The first law of thermodynamics shows how the heat supplied to a system is related to the internal energy and the work done by the system. Most of the useful inventions are based on this law such as heat engines, refrigerators, and air conditioners. 

The mathematical form of the first law of thermodynamics can be stated as for noncyclic process; "The change in internal energy of a system is equal to the summation of amount of heat added to the system from surrounding and work done by the system on the surrounding (or It can also happen between two systems)".
   ➩ { Total energy (E) of the system ＝ constant }
In the above equation, the total energy ∆E is nothing but a sum of kinetic energy, potential energy and other energies present in the molecules of the body, which is also known as internal energy ∆U. Thus, the equation for the first law of thermodynamics is given as;

-------------------(1)
Here,
      ∆U = Change in internal energy (U₂-U₁)
      Q = Amount of heat added to the system
      W = Work done by the system
-------------------(2)
Here,
      ∆U = Change in internal energy (U₂-U₁)
      Q = Amount of heat added to the system
      W = Work done on the system

Q is positive if heat is added to the system, and negative if heat is removed; W is positive if work is done by the system, and negative if work is done on the system. 
The standard unit for all these quantities would be the joule, although they are sometimes expressed in calories or Btu. Equation (1) & (2) shows the finite changes occur within the system or we called as "Finite Form Of First Law Of Thermodynamic". 

According to the equation(1), Whenever heat(Q) is added to the system, the change in total energy of the system (∆U) increases. But whenever the work(W) is done by the system, then the change in total energy of the system decreases. While the differential form of first law of thermodynamic is given as; 
                 ➩ { (U₂-U₁) ＝ dQ - dW } 
                                       -------------------(3)
However, the first law of thermodynamics applies to the system and its surroundings; Not on the system alone. Thus, first law of thermodynamics for any process;
       Change in      ＋     Change in        ＝     0
          Energy               energy of the
    Of the system         surrounding

What Is Heat? How Is It Related To The 1st Law Of Thermodynamics?
When someone touches the hot flames, the thermal energy of the flame enters the body of that person, because the flame is hot as compared to the human body. But think about the second case. When you touch the ice, the case is completely reversed. The thermal energy will pass out of your hand, because your hand is warmer than the ice.
What did you notice from these two examples of heat flow???
 • Heat always flows from higher temperature to lower temperature.
 • Heat flows due to temperature differences between the two objects.
Definition Of Heat: 
"Heat is defined as a flow of thermal energy due to differences in temperatures".

What Is Work? How Is It Related To The 1st Law Of Thermodynamics??
!!!When The Volume Of The System Increases Then The Work Is Done By The System Or When The Volume Of The System Decreases Then The Work Is Done On The System!!!
When can we say that work is done?
When a force is applied to any body and if that body moves in the direction of applied force, then we can say that work is done. During the thermodynamic process, the volume of the system may increase or decrease. The thermodynamic system is doing work on the surrounding or surrounding.

First Law Of Thermodynamics For Cyclic Process 
The initial and final states of the process determine the value of internal energy because it is a state function or variable. As a result, the change in internal energy for a cyclic process with identical initial and final states is zero because all the state properties which is dependent on the initial and final states are zero. In a cyclic process, the initial and final states are same.
!!!Thus, For A Cyclic Process, Heat Added To The System Is Equal To The Work Done By The System!!!
.......Total amount of heat is equal to the total amount of work in a cyclic process........
Cyclic Integral Of    ＝   Cyclic Integral Of  
Work Transfer                Heat Transfer 
∲∆U = ∲δQ – ∲δW = 0  
➩ [ ∲δQ = ∲δW ]
  ----------------(1)
➩ [ ∑Q = ∑W ]
---------------(2)
Equation (1) is known to be an integral form of the first law of thermodynamics. 

Perpetual Motion Machine Of The First Kind- PMM 1
The machine or a device which does not obey this first law of thermodynamics is known as a perpetual motion machine of first kind- PMM 1.
You can see in the picture, the device keeps on rotating on its own. It never stops.
The motion of such devices or machines does not require any input energy, force or something like that.
Even though they keep on producing work.
But wait. How is this possible???
We have seen that energy can’t be created. It can just be transformed from one form to another.
If we are not giving any energy then why does this device keep on rotating? 
This type of machine is impossible. This device does not obey the 1st law of thermodynamics. 
!!!This Is The Reason Why Such Machines Are Known As Perpetual Motion Machines!!!

FEW CONSIDERATION IN FIRST LAW
I have also explained the sign convention for work (W) and heat (Q). You will come to know when we should take the sign of work and heat as positive (+ve) and negative (-ve).
a. If heat is supplied to the system (+Q), then U will increase.
b. If heat is removed from the system (-Q), then U will decrease.
c. If work is done on the system (+W), then U will increase.
d. If work is done by the system (-W), then U will decrease.
e. Internal energy include All Forms Of Energies. It just quantifies the current amount of energy present and the changes in energy.

LIMITATIONS OF THE FIRST LAW OF THERMODYNAMICS
It does quantify the energy transfer that takes place. But this fails to explain about the feasibility of thermal process. For example, heat always flows from hot body to a cold body (that is, in the presence of a heat gradient). The reasons for this (also called as feasibility of process) is not covered in the first law.


FAQs
Que- Is the first law of thermodynamics only applicable to a closed system ??
Its a universal law. You can apply it anywhere and everywhere.
Related
Que- Why is the first law of thermodynamics not enough???
The First Law is restricted to the simple concept that energy is conserved. But it does not account for innumerable observations we make every day that concern the direction in which energy and molecules flow. This is where the Second Law comes in to play. One statement of the Second Law is that it is the Law of Irreversibility.
Que- Why do we wear sweater during winter and not during summer???
In Summer season, the heat enters the body from the surrounding. Thus we feel hot. While, in the winter season, our body loses heat to the surrounding (because in winter, our body is warmer than the surrounding. Remember, heat always flows from higher temperature to lower temperature). This is the reason why we feel cold in the winter season.
         And in order to avoid this heat loss from the body, we have to wear sweater in winter.



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