The volume of a certain gas will increase as the pressure applied to it decreases. This relationship can be modeled using the formula: ar VP V2 = hes it can be used P2 where V, is the initial volume of the gas, P is the initial pressure, P2 is the final pressure and the V2 is the final volume of the gas. If the initial volume of the gas is 500ml and the initial pressure is 12 atm, what is the final volume of the gas if the final pressure is 5 atm? ( Show your solution)
Answers
Answer:
The dimensionless compressibility factor, Z, for a gaseous species is defined as the ratio
Z =
pv
RT
(3.4-1)
If the gas behaves ideally Z = 1. The extent to which Z differs from 1 is a measure of the
extent to which the gas is behaving nonideally. The compressibility can be determined from
experimental data where Z is plotted versus a dimensionless reduced pressure pR and
reduced temperature TR, defined as
pR = p/pc and TR = T/Tc
In these expressions, pc and Tc denote the critical pressure and temperature, respectively. A
generalized compressibility chart of the form Z = f(pR, TR) is shown in Figure 3.4-1 for 10
different gases. The solid lines represent the best curves fitted to the data.
Figure 3.4-1 Generalized compressibility chart for various gases
10
.
It can be seen from Figure 3.4-1 that the value of Z tends to unity for all temperatures as
pressure approach zero and Z also approaches unity for all pressure at very high temperature.
If the p, v, and T data are available in table format or computer software then you should not
use the generalized compressibility chart to evaluate p, v, and T since using Z is just another
approximation to the real data.
10 Moran, M. J. and Shapiro H. N., Fundamentals of Engineering Thermodynamics, Wiley, 2008, pg. 112
3-20
Example 3.4-2 ----------------------------------------------------------------------------------
A closed, rigid tank filled with water vapor, initially at 20 MPa, 520
oC, is cooled until its
temperature reaches 400
oC. Using the compressibility chart, determine
(a) the specific volume of the water vapor in m
3
/kg at the initial state.
(b) the pressure in MPa at the final state.
Compare the results of parts (a) and (b) with values obtained from the thermodynamic table
or software
11
.
Solution ------------------------------------------------------------------------------------------
(a) The specific volume of the water vapor in m
3
/kg at the initial state.
Look up the critical temperature Tc and critical pressure pc of water:
Substance Chemical Formula M (kg/kmol) Tc (K) pc (bar)
Water H2O 18.02 647.3 220.9 0.233
Evaluate the reduce pressured pR and reduce temperatured TR
pR1 = 20/22.09 = 0.91,TR1 = (520 + 273.15)/647.3 = 1.23
Figure E3.4-2 Generalized Compressibility Chart
With these values for the reduced pressure and reduced temperature, the value of Z from
Figure E3.4-2 is approximately 0.83
Z =
pv
RT
=
pMv
RT
v1 = Z1
1
1
RT
Mp
`` v1 = 0.83
8314 N m/kmol K
18.02 kg/kmol
⋅ ⋅
6 2
793.15 K
20 10 N/m
×
= 0.0152 m
3
/
Step-by-step explanation:
Step-by-step explanation:
hi
0.0152m
is the right answer