# Differential form of the First Law

For an infinitesimal process, equation (i) takes the form

δq = dE + δw …….(ii)

a) Change in internal energy is independent of the path taken. So in mathematical terms, an exact differential is always denoted by a notation d, e.g. dE in equation (ii).

b) q and w are not state functions because changes in their magnitude is dependent on the path by which the change is accomplished. Mathematically q & w are not exact differentials and we always write the inexact − differential by δq, δw etc.

c) For a cyclic process, the change in the internal energy of the system is zero because the system is brought back to the original condition.

∮dE = 0

∮δq or ∮δw = i.e. the total work obtained is equal to the net heat supplied.

d) In an isolated system, there is no heat exchange with the surrounding i.e. δq = 0

∴ dE + δW = 0

or δw = − dE

The sign convention: According to latest S.I. convention, w is taken as negative if work is done by the system whereas it is taken as positive if work is done on the system. When heat is given by the system to surrounding it is given as negative sign. When heat is absorbed by the system from the surrounding then positive sign is given.

## Heat, Energy, Work

### Heat

Like work, heat is regarded in thermodynamics as energy in transit across the boundary separating a system from its surroundings. However, quite unlike work, heat transfer results from a temperature difference between system and surroundings, and simple contact is the only requirement for heat to be transferred by conduction. Heat transfer ceases when thermal equilibrium is attained. All other forms of energy can be quantitatively converted into work but heat cannot be completely converted into work without producing permanent changes either in the system or in the surroundings. Heat is an algebraic quantity and is symbolised as Q.

The units of heat are those of work and energy. The sign convention used for a quantity of heat Q is opposite to that used for work. Heat added to a system is given by a positive sign, whereas heat extracted from a system is given negative sign.

Like work Q is not a state function, its work depends on the path which is followed for carrying out the transformation in the state of the system. Heat is, therefore a path dependent quantity.

## Energy

It is the capacity for doing work. Whenever, there is a rearrangement of atoms as in chemical reactions or as in changes in the state of matter (e.g. fusion, vapourisation, sublimation, etc.) energy changes are involved. Energy manifests itself in various forms. For example, the kinetic energy of a body is due to its motion and potential energy of a body is due to its motion and potential energy of a body is due to its position in space. These two forms of energy are little importance for chemical system. The energy which is of great significance from chemical point of view is the internal energy of substance.

The energies acquired by a system in a force field like electric, magnetic, gravitational surface etc. are termed as external energies and are usually not considered as part of the internal energy of the system.

Energy is an extensive property i.e., its magnitude depends upon the quantity of material in the system.

In SI system, the unit of energy is expressed in J or kJ

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