   Chapter 18, Problem 17PS

Chapter
Section
Textbook Problem

Which substance has the higher entropy? (a) dry ice (solid CO2) at −78 °C or CO2(g) at 0 °C (b) liquid water at 25 °C or liquid water at 50 °C (c) pure alumina, Al2O3(s), or ruby (ruby is Al2O3 in which some Al3+ ions in the crystalline lattice are replaced with Cr3+ ions) (d) one mole of N2(g) at 1 bar pressure or one mole of N2(g) at 10 bar pressure (both at 298 K)

(a)

Interpretation Introduction

Interpretation: From the given substances that is dry ice at -78oC or CO2 at 0oC the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

Explanation

Entropy increases in the order solid < liquid < gas.  In the gaseous state, the particles are more random. In solids, the particles have fixed positions and entropy is less. In liquids, there are constraints due to forces between the particles.

Hence, entropy is more for CO2(g)

(b)

Interpretation Introduction

Interpretation: From the given substances that is liquid water at 25oC or liquid water at 50oC the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

(c)

Interpretation Introduction

Interpretation: From the given substances that is pure alumina and ruby the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

(d)

Interpretation Introduction

Interpretation: From the given substances that is 1molofN2(g)at1bar or 1molofN2(g)at10bar the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

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