First law of thermodynamics for open and closed system

First law of Thermodynamics

Closed System : [ Control Mass ]

a. Conservation of mass :

Mass of control mass system remains constant.

i.e. 

b. Conservation of energy :

At state 1 : (i.e. at the beginning)
Internal energy = u₁
Potential energy = gz₁
Kinetic Energy = (1/2) c₁²

 

Note : These are the values in specific case i.e. for unit mass.

At state 2:
Internal energy = u₂
Potential energy = gz₂
Kinetic energy = (1/2) c₂²
 
Let ‘q’ and ‘w’ are the energy interaction from the system. Then, from the principle of conservation of energy, we have,

Then, For non – flow system,

Then,

Open system [ Control Volume ]

a. Conservation of open system :

The rate of change of mass of control volume is the difference of rate of change of mass at the inlet and outlet of the system.

Now, If A₁, c₁ and A₂, c₂ be the area of cross section and velocity at inlet and outlet respectively. Then , the rate of change of volume at inlet and outlet are given by, 

b. Conservation of energy :

Energy at inlet:

Internal energy = u₁
Potential energy = gz₁
Kinetic Energy = (1/2) c₁²
Flow energy = P₁v₁

Energy at outlet:

Internal energy = u₂
Potential energy = gz₂
Kinetic energy = (1/2)c₂²
Flow energy = P₂v₂
Let ‘q’ and ‘w’ are the energy interaction to and from the system.
If ‘ e₁’ and ‘ e₂’ are energy before and after the process inside the control volume.
Then, by conservation of energy,

Now,
For steady flow,