Chapter 4.8, Problem 34P

Interpretation Introduction

Interpretation:

Estimate the values of $\Delta {\underset{\_}{U}}_{vap}$, $\Delta {\underset{\_}{\text{H}}}_{vap}$, $\Delta {\underset{\_}{\text{S}}}_{vap}$ and $C_P^{*}$ for designing a chemical process.

Concept Introduction:

The time independent energy balance for the closed system is given by:

$\Delta U=Q+W_{EC}$

Here, heat is Q, change in internal energy is $\Delta U$, and work expansion or contraction is $W_{EC}$.

Substituting $\Delta U=N\times \Delta {\underset{\_}{U}}_{vap}$ in the above, we get.

$N\times \Delta {\underset{\_}{U}}_{vap}=Q+W_{EC}$

Here, number of mole is N and molar change in internal energy of vaporization is $\Delta {\underset{\_}{U}}_{vap}$.

The work done equation for constant pressure process is given by:

$\begin{array}{c}{W}_{EC}=-{\displaystyle \int PdV}\\ =-P\left(V_{final}-V_{initial}\right)\end{array}$

Here, pressure is P and change in volume is dV.

Use the ideal equation in place of the final volume to find the work done.

$W_{EC}=-P\left(\frac{RT}{P}-V_{initial}\right)$

Calculate the value of $\Delta {\underset{\_}{U}}_{vap}$.

$\Delta {\underset{\_}{U}}_{vap}=\frac{Q+W_{EC}}{N}$

Calculate the molar change in enthalpy using the formula:

$\begin{array}{l}\Delta U=Q+\left(-P\Delta {\underset{\_}{V}}_{vap}\right)\\ \Delta U+P\Delta {\underset{\_}{V}}_{vap}=Q\\ \Delta H_{vap}=Q\end{array}$

Calculate the molar change in entropy of vaporization using the given formula.

$\begin{array}{c}\Delta {\underset{\_}{S}}_{vap}=\frac{\Delta S}{N}\\ =\frac{Q/T}{N}\end{array}$

Calculate the specific heat capacity at constant pressure using the formula:

$\begin{array}{c}Q=N{C}_P^{*}dT\\ =N{C}_P^{*}\left(T_2-T_1\right)\end{array}$