Chapter 3.9, Problem 26P

(A)

Interpretation Introduction

Interpretation:

Determine the initial volume, final volume, work and heat transfer.

Concept Introduction:

Write the expression to calculate the number of moles in nitrogen.

$N=\frac{M}{MW}$

Here, molecular weight of nitrogen is MW and mass of nitrogen is M.

Write the expression to calculate the initial volume.

$V_{initial}=\frac{NR{T}_{initial}}{P_{initial}}$

Here, initial temperature and pressure is $T_{initial}$ and $P_{initial}$, number of moles is N, and gas constant is R.

Write the expression to calculate the final volume.

$V_{final}=\frac{NR{T}_{final}}{P_{final}}$

Here, final temperature and pressure is $T_{final}$ and $P_{final}$ respectively.

Write the energy balance around the compressor.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+W_S+W_{EC}+Q$

Here, time is t, total mass of the system is M, specific internal energy of the system is $\widehat{U}$, velocity of the system is v, height of the system is h, acceleration due to gravity is g, individual quantities of mass added to and removed from the process is ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$, specific enthalpies of streams inlet and outlet is ${\widehat{H}}_{in}$ and ${\widehat{H}}_{out}$, heights at which streams enters and leave the system is $h_{in}$ and $h_{out}$, total expansion or contraction work added throughout the process is $W_{EC}$, total shaft work added throughout the process is $W_S$, and the total heat added throughout the process is Q.

(B)

Interpretation Introduction

Interpretation:

Determine the initial volume, final volume, work and heat transfer.

Concept Introduction:

Write the expression to calculate the initial molar volume by using the van der Waals equation.

$P_{initial}=\frac{R{T}_{initial}}{{\underset{\_}{V}}_{initial}-b}-\frac{a}{{\underset{\_}{V}}_{initial}{}^2}$

Here, constants are a and b respectively.

Write the expression to calculate the initial volume.

$V=\frac{M\underset{\_}{V}}{MW}$

Write the expression to calculate the final molar volume by using the van der Waals equation.

$P_{final}=\frac{R{T}_{final}}{{\underset{\_}{V}}_{final}-b}-\frac{a}{{\underset{\_}{V}}_{final}{}^2}$

Write the expression to calculate the final volume.

$V=\frac{M{\underset{\_}{V}}_{final}}{MW}$