2D3 :  Volume Occupied by 25 kg of R134a at Various Temperatures  6 pts 

Determine the volume occupied by 25 kg of R134a at a pressure of 800 kPa
and the following temperatures: a.) 12^{o}C, b.) 40^{o}C, c.) 70^{o}C, d.) 160^{o}C, e.) 325^{o}C 

Read :  This problem is an exercise in how to read and interpolate values from the Steam Tables.  
It covers the use of the Subcooled Liquid Tables and the Superheated Vapor Tables, but does not involve double interpolation because the pressure value, 800 kPa does appear explicitly in both the Subcooled Liquid and Superheated Vapor Tables.  
Given:  m  25  kg  P  800  kPa  
T_{a}  12  ^{o}C  T_{d}  160  ^{o}C  
T_{b}  40  ^{o}C  T_{e}  325  ^{o}C  
T_{c}  70  ^{o}C  ^{}  
Find:  V  ???  m^{3}  
Assumptions:  None.  
Equations / Data / Solve:  
We need to determine the volume of the system and we are given the mass of R134a in the system.  
We need to determine the specific volume of the system because :  

Eqn 1  
So, for each part of this problem, we must evaluate the specific volume and plug this into Eqn 1 to determine the total volume of the system.  
The first step in determining the specific volume is to determine the phase or phases present in the system. From the R134a Tables, we can obtain the saturation temperature associated with 800 kPa.  
T_{sat}  31.33  ^{o}C  
This makes it easy to determine the phase or phases in the system for each part of the problem.  
If :  T_{sys} > T_{sat}  Then :  The system contains a superheated vapor.  
If :  T_{sys} < T_{sat}  Then :  The system contains a subcooled liquid.  
If :  T_{sys} = T_{sat}  Then :  The system could contain an equilibrium mixture of saturated liquid and saturated vapor.  
Part a.)  The system contains a subcooled liquid. Here are the key data values from the Subcooled Liquid Table of the R134a Tables :  
T (^{o}C)  V (m^{3}/kg)  
10  0.00075236  
12  V_{a}  
20  0.00073517  



Eqn 3  
slope  1.7191E06  (m^{3}/kg)/^{o}C  
V  0.00074892  m^{3}/kg  V  0.018723  m^{3}  
18.723  L  
Part b.)  The system contains a
subcooled liquid. Here are the key
data values from the Subcooled Liquid Table of the R134a Tables : 

T_{b}  40  ^{o}C  No interpolation required !  V  0.00070451  m^{3}/kg  
V  0.017613  m^{3}  
17.613  L  
Part c.)  The system contains a superheated vapor. Here are the key data values from the Superheated Vapor Table of the R134a Tables :  
T_{c}  70  ^{o}C  No interpolation required !  V  0.031340  m^{3}/kg  
V  0.78350  m^{3}  
783.50  L  
Part d.)  The system contains a superheated vapor. Here are the key data values from the Superheated Vapor Table of the R134a Tables :  
T_{d}  160  ^{o}C  No interpolation required !  V  0.042291  m^{3}/kg  
V  1.05726  m^{3}  
1057.26  L  
Part e.)  T_{e}  325  ^{o}C  
^{}  
This temperature is too high for our R134a tables !  
At very high temperatures, most gases behave as Ideal Gases.  
The criterion by which we know whether it is reasonable to approximate real gases as ideal gases is :  

Eqn 4  
The Ideal Gas EOS is : 

Eqn 5  
or : 

Eqn 6  
R  8.314  J/moleK  V  0.006216  m^{3}/mole  
V  6.216  L/mole  
The Ideal Gas EOS does NOT apply because V << 20 L/mole !  
Our only choice is to EXTRAPOLATE from the data in the steam tables.  
That is not very safe and I do not want to encourage you to do this, so I will not do it here.  
The best course of action is to find another data source.  
The NIST Webbook yields:  V  0.060298  m^{3}/kg  
V  1.50744  m^{3}  
1507.4  L  
^{}  
Verify:  No assumptions to verify.  
Answers :  V_{a}  18.7  L  V_{d}  1060  L  
V_{b}  17.6  L  V_{e}  1510  L  
V_{c}  783  L 