Chapter 17, Problem 17.6A

Interpretation Introduction

Interpretation:

The spontaneity of a process depends on several factors; one of the several factors is entropy. When the change in entropy of a process is negative, the process is said to be spontaneous.

Concept introduction:

Entropy is referred to as the 'state of disorder' of a system. Also, entropy is a measure of the energy of atoms and molecules in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities.
When the change in entropy of a process is negative, the process is said to be spontaneous due to increase randomness of the system. When the change in entropy of a process is positive, the process is said to be non-spontaneous due to decrease in randomness of the system. The change in entropy occurs during phase transitions, precipitation reactions etc.
The change in entropy is defined as the difference between the entropies of the final and initial states:

$\Delta S = S_f - S_i.$

Formula to calculate change in entropy

$\Delta S_{ }=C_v ln\left(\frac{T_2}{T_1}\right)+Rln\left(\frac{V_2}{V_1}\right)$

$C_v$ = molar heat capacity at constant volume

$T_1$ = Initial temperature

$T_2$ = Final temperature

$V_1$ = Initial volume

$V_2$ = Final volume

Given:

State A: 1 mol of $N_2$ gas at STP
State B: 1 mol of $N_2$ gas at 273 K in a volume of 11.2 L

To determine:

1. To determine which state has higher entropy in terms of probability.
To determine the change in entropy $(\Delta S)$
2. from State A to State B.