Chapter 6, Problem 6.17P

Interpretation Introduction

Interpretation:

Calculate the final temperature and fraction of system freezes if a small ice crystal is added to seed subcooled pure liquid. Also find the $\Delta S_{total}$ for the process. What is its irreversible features.

Concept Introduction:

After adding small ice crystal in the subcooled pure liquid, it tries to regain its original temperature $0^{\circ }\text{C}$, So the process is two-step process where in first step heating (sensible heat) occurs from temperature $-6^{\circ }\text{C}$ to $0^{\circ }\text{C}$ and in second phase change occurs after the liberation of latent heat. So, the overall heat transferred occurs during process is:

$Q=\Delta H=C_P\Delta T+x\Delta H_{fusion}$

                    .... (1)

Where first term in right side is sensible heat and second term is latent heat, $C_P$ is the specific heat of subcooled liquid water, $\Delta T$ is temperature change during process, $x$ is the fraction of system freezes, $\Delta H_{fusion}$ is the latent heat of fusion of water.

The total entropy change if $\Delta H_{fusion}$ is given,

  $\begin{array}{l}\Delta S=C_P\frac{dT}{T}+\frac{x\Delta H_{fusion}}{T}\\ \Rightarrow \Delta S=C_P\ln \frac{T_2}{T_1}+\frac{x\Delta H_{fusion}}{T_2}\end{array}$