Chapter 10, Problem 10.80PAE

Interpretation Introduction

Concept Introduction:

Gibb’s free energy is a state function which predicts whether a process is spontaneous or not at conditions of constant pressure and temperature. Gibb’s free energy change for a process at constant temperature is defined as:

$\Delta G=\Delta H-T\Delta S$

Where $\Delta S$ is the total change in the entropy of the system and $\Delta H$ is the total change in the enthalpy of the system. For a spontaneous process $\Delta G$ must be negative.

Entropy is defined as the measure of randomness or disorder in a system.

Entropy of a system is defined statistically on a microscopic level. In statistical mechanics the number of microstates or energy states that is the number of ways in which these microscopic particles acquire same energy is determined.

The number of microstates for a particular energy is denoted as Omega (O). And the entropy is then related to number of microstates by the equation:

$S=k_{\text{B}}\ln \Omega$

Where, $k_{\text{B}}$ is Boltzmann’s constant.

More random arrangements of particles of a system would increase the number of microstates possible for the system. And so entropy of any system increases if it moves towards more random distribution of particles constituting the system.

When a system is heated to a higher temperature, the total energy available to the molecules increases and some portion of molecules can now move at higher speeds. The system can now distribute its energy in more number of ways. Hence heating a system increases it entropy.

In a solid the particles are held together rigidly. When it is melted to form a liquid the particles gain energy and are free to move. The entropy of the system increases.

When you boil a liquid to form vapor, again the particles which are confined to move in a small space in a liquid are more randomly distributed in the vapor phase.