CHEMICAL ENGINEERING

SECTION 2

Flow of Fluids — Energy and

Momentum Relationships

PROBLEM 2.1

Calculate the ideal available energy produced by the discharge to atmosphere through a
nozzle of air stored in a cylinder of capacity 0.1 m^3 at a pressure of 5 MN/m^2. The initial
temperature of the air is 290 K and the ratio of the specific heats is 1.4.

Solution

From equation 2.1: dUDυqυW. For an adiabatic process:υqD0anddUDυW,
and for an isentropic process: dUDCvdTDυWfrom equation 2.25.

AsDCp/CvandCpDCvCR(from equation 2.27),CvDR/
 1

∴ WDCvTDRT/
 1 D RT 1 RT 2 /
 1

and: RT 1 DP 1 v 1 andRT 2 DP 2 v 2 and hence:WD
P 1 v 1 P 2 v 2 /
 1

P 1 v

1 DP^2 v



2 and substituting forv^2 gives:

WD[

P 1 v 1 /

 1 ] 

1 

P 2 /P 1 

^1 /

and: UDWD[
P 1 v 1 /
 1 ][
P 2 /P 1
^1 /1]

In this problem:

P 1 D5MN/m^2 ,P 2 D 0 .1013 MN/m^2 ,T 1 D290 K, andD 1. 4.

The specific volume,v 1 D
22. 4 / 29
290 / 273
0. 1013 / 5 D 0 .0166 m^3 /kg.

∴ WD[
5 ð 106 ð 0. 0166 / 0 .4][
0. 1013 / 50.^4 /^1.^4 1]D 0. 139 ð 106 J/kg

Mass of gasD
0. 1 / 0. 0166 D 6 .02 kg

∴ UD
0. 139 ð 106 ð 6. 20 D 0. 84 ð 106 Jor840 kJ

PROBLEM 2.2

Obtain expressions for the variation of: (a) internal energy with change of volume,
(b) internal energy with change of pressure, and (c) enthalpy with change of pressure, all
at constant temperature, for a gas whose equation of state is given by van der Waals’ law.

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