# First Law of Thermodynamics

First law of thermodynamics is also known as law of conservation of energy. It can be stated in different ways.

• The net energy of the universe (system + surrounding) always remains constant.
• The total energy change of a isolated system remains constant throughout the change though it changes from one form to another form.
• If heat is disappeared in a change, an equivalent amount of work is produced or can be done through it.
• Energy can neither be destroyed nor can be created but can be changed from one form to another form.
• The total sum of mass and energy of a system remains constant.

Derivation of First Law of Thermodynamics:

To formulate the law, consider a gaseous closed system  fitted with weightless and frictionless piston.

Let, E1 the internal energy of the system I. When ΔQ amount of heat is supplied to the system, the total energy before change = E1 + ΔQ. When the system is changed to state II by the application of ΔQ quantity of heat, the internal energy also changes to E2. In this change,  ΔW amount of work is done. After change, the total energy becomes E2 + ΔW. Now, from the first law of thermodynamics.

E1 + ΔQ = E2 + ΔW

or, ΔQ = E2 – E1 + ΔW

or, ΔQ = ΔE + ΔW

or, dQ = dE + dW

The equation (i) shows that when heat is supplied to the system, some of its amount is used to increase the internal energy of the system and the remaining is used in the form of work. Again the work done by this gaseous system is at constant pressure due to the expansion in volume.   Now,

ΔW = P ΔV

Now, the equation (i) becomes,

ΔQ = ΔE + P ΔV

Further at constant pressure, ΔQ  = ΔH, i.e.,

ΔQp =  ΔH = Enthalpy change of  the system.

Therefore, equation (i) becomes,

ΔH = ΔE + PΔV

where, ΔH = Enthalpy change

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