Physical significance of Entropy

The entropy of a substance is real physical quantity and is a definite function of the state of the body like pressure, temperature, volume of internal energy.

It is difficult to form a tangible conception of this quantity because it can not be felt like temperature or pressure. We can, however, readily infer it from the following aspects:

1. Entropy and unavailable energy

The second law of thermodynamics tells us that whole amount of internal energy of any substance is not convertible into useful work. A portion of this energy which is used for doing useful work is called available energy. The remaining part of the energy which cannot be converted into useful work is called unavailable energy. Entropy is a measure of this unavailable energy. In fact, the entropy may be regarded as the unavailable energy per unit temperature.

I.e.

$\text{Entropy} = \dfrac{\text{Unavailable energy}}{\text{Temperature}}$

or, $Unavailable \hspace{2mm}energy \hspace{2mm} = Entropy \times Temperature$

The concept of entropy is of great -value and it provides the information regarding structural changes accompanying a given process.

2.  Entropy and disorder

Entropy is a measure of the disorder or randomness in the system. When a gas expands into vacuum, water flows out of a reservoir, spontaneous chain reaction takes place, an increase in the disorder occurs and therefore entropy increases.

Similarly, when a substance is heated or cooled there is also a change in entropy. Thus increase in entropy implies a transition from on ordered to a less ordered state of affair.

3. Entropy and probability

Why is disorder favoured? This can be answered by considering an example, when a single coin is flipped, there is an equal chance that head or tail will show up. When two coins are flipped, there is a chance of two heads or two tails showing up but there are double chance of occurrence of one head and one tail. This shows that disorder is more frequent than order.

Changes in order are expressed quantitatively in terms of entropy change, $\Delta S$. How are entropy and order in the system related? Since a disordered state is more probable for systems than of order(see figure), the entropy and thermodynamic probabilities are closely related.

Order and probality

Features of entropy:

(1)    It is an extensive properly and a state function

(2)    It’s value depends upon mass of substance present in the system

(3)    $\Delta S = S_{final}- S_{initial}$

(4)    At equilibrium $\Delta S = zero$

(5)    For a cyclic process $\Delta S = 0$

(6)    For natural process $\Delta S > 0$ i.e Increasing.

(7)    For a adiabatic process $\Delta S$ zero

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