# First Law of Thermodynamics and its Application to Different Processes

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### Zeroth Law of Thermodynamics:

#### Statement:

• If two bodies (say A and B) are in thermal equilibrium of the third body (say C) then body A and B will also be in thermal equilibrium with each other

#### Significance of the Law:

• The common use of the thermometer in comparing the temperature of any two or more systems is based on the zeroth law of thermodynamics.

### First Law of Thermodynamics:

#### Statement:

• Different forms of the first law of thermodynamics are as follows
1. Energy can’t be created nor destroyed but it can be converted from one form into the other (or forms) or into work.
2. When a quantity of energy of one kind disappears, then an equivalent amount of energy of another kind makes its appearance.
3. It is impossible to make a perpetual motion machine which would produce work without consuming energy.
4. The total amount of energy of an isolated system remains constant, it may change from one form to another.
5. The energy of the universe remains constant.
6. For a system in contact with the surroundings, the sum of energies of the system and its surrounding remains constant however differently it may be shared between the two.

#### Mathematical Statement of the First Law:

• Consider the system in state I ( initial state) with internal energy U1. It is converted into state II (final state) with internal energy U2 by supplying  ‘q’  amount of heat to it. During this process, some work “W” is done by the system on the surroundings. Heat absorbed by the system is used for a)  increasing internal energy of a system.  and b)  to do some mechanical work  “W”.  I
• Now , Change in the internal energy of the system is equal to the heat supplied plus Work done.

Thus, Final internal energy =  U2  = U1 +   q  +  WHence

∴   (U2  – U1)   =      q  +  W

∴   ΔU = q   +  W

In the pressure-volume type of work  W  =  PΔV

∴   ΔU  =  q +  PΔV

This is the mathematical equation of the first law of thermodynamics.

### Sign Conventions for q, W, and ΔU:

• When heat is absorbed by the system q is positive.
• When heat is rejected or given out by the system q is negative.
• When the work is done on the system by surroundings (Work of compression) then W is positive.
• When the work is done by the system on the surroundings (Work of expansion) then, W is negative.
• When there is an increase in internal energy of the system ( increase in temperature) ΔU is positive.
• When there is a decrease in internal energy of the system ( decrease in temperature) ΔU is negative.

#### Isothermal Process:

• Internal energy is a function of temperature. As the temperature is constant, the internal energy is also constant. Hence there is no change in internal energy.     ΔU = 0

By the first law of thermodynamics,

ΔU = q   +  W

∴  0 = q   +  W

∴ q = -W or W = – q

• Thus in isothermal process heat absorbed is entirely used for doing work on the surroundings or the work done by the surrounding at constant pressure results in the release of the heat (energy) by the system.

• In adiabatic process there is no exchange of heat      q = 0

By the first law of thermodynamics

ΔU = q   +  W

ΔU = 0   +  W

∴   W =  q

• Thus the increase in internal energy of a system is due to work done by the surroundings on the system or work done by the system on the surroundings is due to the expense of internal energy of the system.

#### Isochoric Process:

• In isochoric process there is no change in volume   ΔV = 0,  Thus the work done W = PDV = 0

By the first law of thermodynamics,

ΔU = q   +  W

∴ ΔU = q   +  0

∴ ΔU = q

• Thus the increase in internal energy of a system is due to absorption of the heat from the surroundings or the decrease in internal energy of a system is due to release of the heat from the system to the surroundings.

#### Isobaric Process:

• In isobaric process, there is no change in pressure   ΔP = 0 Thus work done W = – Pext ΔV

By the first law of thermodynamics,

ΔU = q   +  W

∴ ΔU = q   – Pext ΔV

• Thus the increase in internal energy of a system is due to the absorption of the heat from the surroundings or the decrease in internal energy of a system is due to release of the heat from the system to the surroundings.

#### Note:

• Most of the chemical reactions take place at constant pressure.

### Second Law of Thermodynamics:

#### Statement:

• Heat cannot be completely converted into an equivalent amount of work without producing permanent changes either in the system or its surroundings. or The spontaneous flow of heat is always unidirectional, from higher temperature to lower temperature.
• We observe that heat flows from the hot end of a metal rod flows to its cold end. The opposite flow of heat is not taking place.
• The first law (law of conservation of energy) allows heat flow from cold end to hot end. It is possible when heat lost by the cold end is equal to the heat gained by hot end. Thus energy is conserved. But such heat transfer is not possible. Thus the first law of thermodynamics is insufficient to put a restriction on the direction of the heat flow.4. To overcome the deficiency of the first law, the second law of thermodynamics is proposed using human experience.
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