Definition of Law of Conservation Energy
The first law of thermodynamics principles states the conservation of energy of our universe. Study of this conservation law provides the calculation formula of heat change and transfer and internal energy and work done for the cyclic, isothermal, isochoric process and isolated system in thermodynamics and the definition of this law is,
Energy can neither be created nor be destroyed but it may be transferred one form to another.
In other words, when one form of energy disappears, an exact and same amount of other form appears. Thus the net amount of energy in our universe must be constant.
Law of Conservation of Energy Formula
Let q amount of heat supplied to the system containing one-mole gas in a cylinder fitted with a frictionless weightless moveable piston.
At constant pressure, the gas expands from V1 to V2 and the temp changes from T1 to T2. Thus according to 1st law of thermodynamics
q = dU + w
where dU = change of internal energy
If the work restricted to pressure-volume work than the work performed for this system w = PdV.
∴ q = dU + PdV
But U = ∫(T, V)
Putting this value in the energy law
But at constant volume
where Cv = molar heat capacity at constant V.
Thus the generalized mathematical formula of the first law of thermodynamics energy transfer for n mole of a gas
Thermodynamics First Law of Ideal Gases
The thermodynamics equation of state
From ideal gas law
Thus the mathematical form of the first law of thermodynamics for the ideal gas
q = nCVdT + pdV
Thermodynamics First Law of real gases
Van der Waals equation for n mole real gases
Thus from the first law thermodynamics
Example of Conservation of Energy
For an isolated system, the value of q and w are zero since no interaction of the system with the surroundings can take place. Hence we can conclude that the value of the energy function of an isolated system is constant.
For example, this is another principles of conservation of energy and this states as
No matter what changes of state of an isolated system, thus the value of energy function always constant.
Change in Internal Energy Formula Thermodynamics
Internal energy changes in the cyclic process
dU = 0
Thus according to the first law
q = w
Therefore, form the conservation law of thermodynamics, heat is completely converted into work for the cyclic process.
Heat change in the isothermal process
Internal energy change in the isothermal process for the ideal gas
dU = nCVdT = 0
∴ q = w
Therefore thermodynamics heat is completely converted into work for the ideal gas in the isothermal process.
Internal Energy in the Isochoric Process
Volume change in isochoric process
dV = 0
The 1st law of thermodynamics when dV = 0
q = dU = nCVdT
Thus heat change to an isochoric process only increases the internal energy or temperature of the system.
Internal energy change in an isolated system
In an isolated system, neither energy nor matter can be transfer to or from it.
∴ q = 0 for isolated system
From the 1st law of thermodynamics
0 = dU + w
or, w = -dU
Therefore, from this conservation law of thermodynamics, an isolated system, internal energy uses for the work done by the system.