Example Problem with Complete Solution

2D-3: Volume Occupied by 10 kg of Water at Various Temperatures 6 pts
Determine the volume occupied by 10 kg of water at a pressure of 10 MPa and the following temperatures:
a.) Ta 5 oC        
b.) Tb 200 oC        
c.) Tc 400 oC        
d.) Td 800 oC        
e.) Te 1500 oC        
f.) Tf -10 oC        
               
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, 10 Mpa does appear explicitly in both the Subcooled Liquid and Superheated Vapor Tables.
Given : m 10 kg
P 10 MPa
T see the problem statement, above.
Find : V ??? m3
Solution : We need to determine the volume of the system and we are given the mass of water in the system.
We need to determine the specific volume of the system because :
equation 1 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 steam tables, we can obtain the saturation temperature associated with 10 Mpa.
Tsat 311.1 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 Steam Tables :
T (oC) V (m3/kg)
0.01 0.0009952
20 0.0009973
equation 2 Eqn 2
equation 3 Eqn 3
slope 1.1E-07 (m3/kg)/oC
V 0.0009957 m3/kg V 0.009957 m3
Part b.) The system contains a subcooled liquid.  Here are the key data values from the Subcooled Liquid Table of the Steam Tables :
Tb 200 oC V 0.0011482 m3/kg
No interpolation required !
V 0.011482 m3
Part c.) The system contains a superheated vapor.  Here are the key data values from the Superheated vapor Table of the Steam Tables :
Tc 400 oC V 0.02644 m3/kg
No interpolation required !
V 0.26436 m3
Part d.) The system contains a subcooled liquid.  Here are the key data values from the Subcooled Liquid Table of the Steam Tables :
Td 800 oC V 0.04863 m3/kg
No interpolation required !
V 0.48629 m3
Part e.) Te 1500 oC
This temperature is too high for our steam tables !
At very high temperatures, most gases behave as Ideal Gases.
The criterion by which we know it is reasonable to approximate real gases as ideal gases is :
equation 4 Eqn 4
The Ideal Gas EOS is : equation 5 Eqn 5
or : equation 6 Eqn 6
R 8.314 J/mole-K V 0.001474197 m3/mole
V 1.47 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.
Even the NIST Webbook only provides data up to 1001.9oC !
This is not a good question !
Part f.) Tf -10 oC
This value is too low for the Subcooled or Compressed Liquid Table !
I do not recommend that you extrapolate.
This is not a good question !