Laws of Conservation: Mass, Energy & Momentum Conservation

Before defining conservation laws, we should have some basic understanding about 'System' and 'surrounding'. 
A 'System' is defined as a region in space where we focus our attention (or chosen for the study or analysis). While the region outside the system is called as 'Surrounding' and the summation of system and surrounding are called as 'Universe'. The real or imaginary surface which seperate the system from its surrounding is called as 'Boundary'.
      Consider any region of space enclosed for the purpose of accounting these conservation laws by a fictitious surface denoted as "Control Surface" and the volume within the the surface is referred as "Control Volume".

Conservation laws/ laws of conservation states that "A certain physical properties (or measurable quantities) does not change in the course of time within an isolated system". 
An isolated system is a system that does not interact with its surroundings in any way. And, these quantities which do not change over a period of time within an isolated system are called "Conserved Quantities". 
Examples of these quantities are mass, energy and momentum etc. And the conservation laws associated with these three conserved quantities are called the "Fundamental Conservation Laws". These three fundamental conservation laws are widely applied in chemical engineering problems or physics. 

Let us now understand all these laws one by one;
Law of conservation of mass
The law of conservation of mass states that- 
"The total mass of an isolated system is constant over time. That means mass can neither be created nor destroyed. It can only be transfer from one place to another". 
Therefore, in case of a chemical reaction the total mass of the reactants must be equal to the total mass of the products. 
For Example;
         CH₄    +    2O₂    ➝      CO₂      +     2H₂O          
     (12+4×1)   (2×32)       (12+16×2)   2(2×1+16)
             (16+64)                          (44+36)         
             = 80kg                            = 80kg
While for a case of flowing system, the mass balance can be written as ( Generally, unsteady state behaviour);
  Rate of mass  ＝  Rate of mass  十     Rate of  
      flow in                 flow out           Accumulation 
And for a steady state system in which there is no accumulation of mass within a system, mass balance can be written as;   
   Rate of mass flow in = Rate of mass flow out

Law of conservation of energy
(Energy is defined as the ability to do work)
The law of conservation of energy states that- "the total energy of an isolated system (such as universe) is constant over time. That means, energy can neither be created nor destroyed. It can only be transform from one of energy to other, but the total amount of energy never changes". 
The forms of energies are kinetic energy, potential energy, thermal energy, electrical energy, rotational energy and mechanical energy etc. Mechanical energy is defined as the sum of kinetic energy and gravitational potential energy. 
For Example- 
1) First, the ball has only potential energy due to its rise from the ground. When the ball starts rolling, its potential energy is converted into kinetic energy and then finally all its kinetic energy is converted back into potential energy.

2) Dams, which hold water at a higher level and then drain water at a lower level. Initially, when water is placed at a height (h), it has potential energy due to its height. And when water falls down, due to the motion of water, its potential energy gets converted into kinetic energy. And after some time, when the water reaches the surface of the lower level, all its kinetic energy is converted back into potential energy.   

➛ Whereas the principle of the law of conservation of energy is defined for a system in the following way;
For steady state,
     ➩ ( Total energy in) ＝ ( Total energy out)
For unsteady state,
 ➩ Total flow ＝   Total flow  十      Rate of
       of energy        of energy       accumulation
        into the          out of the           of energy
        system             system           within system   


Law of conservation of momentum
Momentum is defined as the product of mass and velocity of an object. It is denoted by a symbol of 'p'. In mathematical formulation, momentum is given as,
         ➩ Momentum = mass × velocity
The law of conservation of momentum states that- "The total amount of momentum will remain constant within an isolated system and will never change over time in the absence of external force. This means that the momentum at the beginning of the reaction will be the same as the momentum at the end of the reaction".
 
While in physics, law of conservation of momentum states that- "When two objects collide, the momentum before the collision and the momentum after the collision must be the same in absence of external force".
For Example- 
Consider two objects, Object -1 and Object-2. Both are colliding with each other in an isolated system without any external force, out of which Object -1 is in motion state and Object-2 is in stationary state. When object -1 collides with Object-2, the momentum of Object -1 starts decreasing and the momentum of object-2 starts increasing. The more the momentum of Object -1 decreases, the more the momentum of Object-2 increases. And thus, the total momentum remains conserved. 
Here, the momentum lost by Object -1 is equal to the momentum gained by Object-2.
➛ Conservation law of momentum is applied to a system can be written as,
   ➩ Total momentum ＝ Total momentum
         before collision           after collision

Momentum problems 
Que- What is the momentum of a 45kg boulder rolling at 3.5m/s??
Solve- As we know that,
  ➩ Momentum = mass×velocity of an object
  ➩ momentum, p = m × v
                                 = 45 × 3.5
                                 = 157.5 kg-m/s

Que- What is the mass of a boulder that is rolling at 4.7m/s and has a momentum of 891 kg-m/s ??
Solve- We know that,
   ➩ Momentum = mass×velocity of an object  
   ➩ momentum, p = m × v
   ➩ 891 = mass × 4.7
   ➩ Mass of a boulder, m = 189.57 kg


Hope you have found this article helpful!!
Let me know what you think about CONSERVATION LAWS. Feel free to comment if you have any queries.!!

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