# Example Problem with Complete Solution

2D-3 : Volume Occupied by 25 kg of R-134a at Various Temperatures 6 pts
Determine the volume occupied by 25 kg of R-134a at a pressure of 800 kPa and the following temperatures:
a.) -12oC, b.) -40oC, c.) 70oC, d.) 160oC, e.) 325oC

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
Ta -12 oC Td 160 oC
Tb -40 oC Te 325 oC
Tc 70 oC
Find: V ??? m3
Assumptions: None.
Equations / Data / Solve:
We need to determine the volume of the system and we are given the mass of R-134a 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 R-134a Tables, we can obtain the saturation temperature associated with 800 kPa.
Tsat 31.33 oC
This makes it easy to determine the phase or phases in the system for each part of the problem.
If : Tsys > Tsat Then : The system contains a superheated vapor.
If : Tsys < Tsat Then : The system contains a subcooled liquid.
If : Tsys = Tsat 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 R-134a Tables :
T (oC) V (m3/kg)
-10 0.00075236
-12 Va
-20 0.00073517
Eqn 3
slope 1.7191E-06 (m3/kg)/oC
V 0.00074892 m3/kg V 0.018723 m3
18.723 L
Part b.) The system contains a subcooled liquid.  Here are the key data values from the Subcooled Liquid Table of the
R-134a Tables :
Tb -40 oC No interpolation required ! V 0.00070451 m3/kg
V 0.017613 m3
17.613 L
Part c.) The system contains a superheated vapor.  Here are the key data values from the Superheated Vapor Table of the R-134a Tables :
Tc 70 oC No interpolation required ! V 0.031340 m3/kg
V 0.78350 m3
783.50 L
Part d.) The system contains a superheated vapor.  Here are the key data values from the Superheated Vapor Table of the R-134a Tables :
Td 160 oC No interpolation required ! V 0.042291 m3/kg
V 1.05726 m3
1057.26 L
Part e.) Te 325 oC
This temperature is too high for our R-134a 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/mole-K V 0.006216 m3/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 m3/kg
V 1.50744 m3
1507.4 L
Verify: No assumptions to verify.
Answers : Va 18.7 L Vd 1060 L
Vb 17.6 L Ve 1510 L
Vc 783 L