Engineering Chemistry S Datta

THERMODYNAMICS 75
the disorder and irreversibility and when equilibrium is reached, it has the maximum disorder.
Thus, the entropy of the system goes on increasing and reaches a maximum value at equilibrium.
For example, if a gas with strong odour is let loose at the corner of a room, the odour of the gas
spreads all over the room randomly and equilibrium is reached when the entropy also becomes
maximum.
Highlights:
• Prediction of direction of changes is possible with a thermodynamical quantity
known as entropy (S).
• A spontaneous change occurs in the direction leading to a total increase of entropy.
• It is convenient to calculate total entropy change in two parts. (i) the entropy
change of the system and the entropy change of the surroundings i.e.,
∆S total
= ∆S system
+ ∆S surroundings
.
• Gases generally have higher entropies than liquids.
• Entropy is a state function dependent on P, V, T and path independent.
• If system absorbs heat, entropy increases and vice-versa.
• Any irreversible process is accompanied by increase in entropy. As all spontaneous
processes are irreversible, the entropy of the universe is ever increasing.
• Entropy is a measurement of randomness of a system.
• From experience we can say, disordered form is more probable than ordered form.
So, increase of randomness enhances thermodynamic probability. Boltzmann
expressed this idea by the relation, S = k ln w, where S = entropy, k = Boltzmann
constant, w = thermodynamic probability.
As w is always greater than one, w increases when S increases.
Conversely, when an order to a system is brought, the entropy of the system decreases.
For example, solidification of a liquid brings about orderly state and thereby entropy decreases.
In any system, only a part of the total energy is made available for useful work, some
energy is always dissipated i.e., wasted. The energy unavailable as work is proportional to the
increase of entropy. The higher the entropy, the less the availability of work. Thus, entropy
signifies unavailable form of energy of the system during transformation of heat into work.
Entropy of an ideal gas
In the case of a reversible expansion of an ideal gas in a container as in Fig. 4.3, the
container is fitted with a frictionless movable piston at constant pressure P. The volume of the
gas changes from V 1
to V 2
. Since the process is reversible, the pressure on the gas is
approximately equal to the external pressure P.
Hence, from 1st law of thermodynamics,
dq = dE + dW = dE + P dV.
...(III)
Dividing both the sides of the equation (III) by T,
dq dE
PdV
= +
T T T
∴ dS = C v
. dT T + R dV V .