# First Law of Thermodynamics

#### First Law of Thermodynamics:

The first law of thermodynamics is also called the law of conservation of energy. It may be stated as-

1st Statement- Energy can neither be created nor destroyed in this universe although it may change from one form to another.

2nd Statement- The total energy of an isolated system remains constant although it may change from one form to another.

3rd Statement- If energy disappears in one form, it must reappear in exactly equivalent quantity of some other form.

4th Statement- It is impossible to construct a perpetual motion machine that can work without consuming any energy.

#### Mathematical Statement of First Law of Thermodynamics:

The mathematical expression representing relationship between heat, work and internal energy is called the mathematical statement of the first law of thermodynamics.

Let a system has initial internal energy equal to U1. Let the system absorbs ‘q‘ amount of heat from the surroundings and lets ‘w‘ amount of work is done on the system. Then final internal energy of the system (U2) becomes equal to U1 + q + w.

Then U2 = U1 + q + w

U2 – U1 = q + w

ΔU = q + w

This is the mathematical expression of first law of thermodynamics. Thus,

• If w = 0; then ΔU = q i.e. increase in internal energy of the system is equal to the quantity of heat absorbed by the system. Similarly, a decrease in internal energy of the system is equal to the quantity of heat liberated by the system.
• If q =0; then ΔU = w i.e. under adiabatic conditons, if work is done by the system, its internal energy will decrease but if work is done on the system, its internal energy will increase.
• If ΔU = 0, then q = -w i.e. when there is no change in internal energy, heat absorbed by the system is equal to the work done by the system.

#### Application of First Law of Thermodynamics:

Some applications of the first law of thermodynamics are-

• It gives a relationship between heat, work and internal energy of a system. ΔU = q + w.
• It helps to find internal energy changes and enthalpy changes of different processes.
• A direct consequence of the law of conservation of energy is the Hess’s law of constant heat summation, which states, “The total enthalpy changes in a chemical reaction always remains constant whether the reaction takes place in one step or in several steps”.

#### Limitations of First Law of Thermodynamics:

The first law of thermodynamics has some limitations-

• This law does not tell us the direction in which the process will occur i.e. it fails to explain why a change occurs spontaneously in one direction but not in the other.
• The first law of thermodynamics does not tell whether a change or a process is spontaneous or not.
• It is well known fact that heat energy cannot be completely transferred into work without producing some change elsewhere. The first law of thermodynamics fails to explain this fact.

#### What is Internal Energy?

Every system is associated with different forms of energy i.e. translational energy, vibrational energy, rotational energy, bond energy, electronic energy, nuclear energy etc. The sum total of energy possessed by constituent particles of the system is called the internal energy or intrinsic energy. It is denoted by the symbol U.

##### Characteristics of Internal Energy:
• Internal energy is an extensive property because it depends upon the amount of the substances present in the system.
• The internal energy of a system is a state function. It depends only upon the state variables (T, P, V) of the system.
• The change in internal energy is denoted by ΔU and it is defined as the difference between the internal energies of the final and initial states of the system i.e. ΔU = Ufinal – Uinitial.

Change in internal energy, ΔU is equal to the amount of heat absorbed or liberated during the process at a constant temperature and constant volume i.e. ΔU = qv.