Chapter 5, Problem 5.39NP

(a)

Interpretation Introduction

Interpretation:

The value of $\Delta S$ needs to be determined, if 1.00 mol of liquid water is heated from 0.00 ⁰C to 10 ⁰C at constant pressure. C_P,m = 75.3 JK-¹mol-1

Concept Introduction :

The formula to calculate the change in entropy at constant pressure:

  $\Delta S=n{\displaystyle \underset{{\text{T}}_{\text{i}}}{\overset{{\text{T}}_{\text{f}}}{\int }}\frac{{\text{C}}_{\text{P,m}}}{\text{T}}\text{dT}}\text{ ------- (1)}$

Here $\Delta S$ = Change in entropy

T_f = Final Temperature

T_i = Initial Temperature

C_p,m = molar heat capacity at constant pressure

n = number of moles

(b)

Interpretation Introduction

Interpretation:

The value of $\Delta S$

for the transformation H₂O(s, 0 ⁰C): H₂O(g, 100⁰C) needs to be determined.

Concept Introduction :

The relation for change in entropy for phase change from solid to vapor state is as follows:

  $\Delta \text{S = }\frac{\Delta H_{fusion}}{T_{fusion}}+n{\displaystyle \underset{T_{fusion}}{\overset{T_{boiling}}{\int }}\frac{C_{p,m}}{T}dT+\frac{\Delta H_{vaporization}}{T_{boiling}}\text{ ------ (2)}}$

Here

  $\Delta H_{fusion}$ = Enthalpy of fusion

T_fusion = Fusion Temperature

T_boiling = Boiling temperature

  $\Delta H_{vaporization}=\text{ Enthalpy of vaporization}$