# Tutorial¶

This tutorial will guide you in the basic use of ThermoState. The ThermoState package is designed to ease the evaluation of thermodynamic properties for common substances used in Mechanical Engineering courses. Rather than looking up the information in a table and interpolating, we can input properties for the states directly, and all unknown values are automatically calculated.

ThermoState uses CoolProp and Pint to enable easy property evaluation in any unit system. The first thing we need to do is import the parts of ThermoState that we will use. This adds them to the set of local variables

[1]:

from thermostate import State, Q_, units


## Pint and Units¶

Now that the interface has been imported, we can create some properties. For instance, let’s say we’re given the pressure and temperature properties for water, and asked to determine the specific volume. First, let’s create variables that set the pressure and temperature. We will use the Pint Quantity function, which we have called Q_. The syntax for the Q_ function is Q_(value, 'units').

[2]:

p_1 = Q_(101325, 'Pa')


We can use whatever units we’d like, Pint supports a wide variety of units.

[3]:

p_1 = Q_(1.01325, 'bar')
p_1 = Q_(14.7, 'psi')
p_1 = Q_(1.0, 'atm')


Another way to specify the units is to use the units class that we imported. This class has a number of attributes (text following a period) that can be used to create a quantity with units by multiplying a number with the unit.

units.degR
#     ^^^^
# This is the attribute


Let’s set the temperature now. The available units of temperature are degF (fahrenheit), degR (rankine), degC (celsius), and K (kelvin).

[4]:

T_1 = 460*units.degR
T_1 = 25*units.degC
T_1 = 75*units.degF
T_1 = 400*units.K


The two ways of creating the units are equivalent. The following cell should print True to demonstrate this.

[5]:

Q_(101325, 'Pa') == 1.0*units.atm

[5]:

True


Note the convention we are using here: the variables are named with the property, followed by an underscore, then the number of the state. In this case, we are setting properties for state 1, hence T_1 and p_1.

## ThermoState¶

Now that we have defined two properties with units, let’s define a state. First, we create a variable to hold the State and tell ThermoState what substance we want to use with that state. The available substances are:

• water
• air
• R134a
• R22
• propane
• ammonia
• isobutane
• carbondioxide
• oxygen
• nitrogen

Note that the name of the substance is case-insensitive (it doesn’t matter whether you use lower case or upper case). It is often easiest to set the name of the substance in a variable, like:

[6]:

substance = 'water'


Now we need to create the State and assign values for the properties. Properties of the state are set as arguments to the State class, and they must always be set in pairs, we cannot set a single property at a time. The syntax is

st = State(substance, property_1=value, property_2=value)


Warning

Remember that two independent and intensive properties are required to set the state!

To demonstrate, we will set the T and p properties of the state and set them equal to the temperature and pressure we defined above. Note that the capitalization of the properties is important! The p is lower case while the T is upper case (lower case t means time).

[7]:

print('T = {}, p = {}'.format(T_1, p_1))

T = 400 kelvin, p = 1.0 atmosphere

[8]:

st_1 = State(substance, T=T_1, p=p_1)


Note again the convention we are using here: The state is labeled by st, then an underscore, then the number of the state.

The variables that we use on the right side of the equal sign in the State function can be named anything we want. For instance, the following code is exactly equivalent to what we did before.

[9]:

luke = Q_(1.0, 'atm')
leia = Q_(400.0, 'K')
print('Does luke equal p_1?', luke == p_1)
print('Does leia equal T_1?', leia == T_1)
st_starwars = State(substance, T=leia, p=luke)
print('Does st_starwars equal st_1?', st_starwars == st_1)

Does luke equal p_1? True
Does leia equal T_1? True
Does st_starwars equal st_1? True


Warning

To avoid confusing yourself, name your variables to something useful. For instance, use the property symbol, then an underscore, then the state number, as in p_1 = Q_(1.0, 'atm') to indicate the pressure at state 1. In my notes and solutions, this is the convention that I will follow, and I will use st_# to indicate a State (e.g., st_1 is state 1, st_2 is state 2, and so forth).

In theory, any two pairs of independent properties can be used to set the state. In reality, the pairs of properties available to set the state is slightly limited because of the way the equation of state is written. The available pairs of properties are

• Tp
• Ts
• Tv
• Tx
• pu
• ps
• pv
• ph
• px
• uv
• sv
• hs
• hv

The reverse of any of these pairs is also possible and totally equivalent.

By setting two properties in this way, the State class will calculate all the other properties we might be interested in. We can access the value of any property by getting the attribute for that property. The available properties are T (temperature), p (pressure), v (mass-specific volume), u (mass-specific internal energy), h (mass-specific enthalpy), s (mass-specific entropy), x (quality), cp (specific heat at constant pressure), cv (specific heat at constant volume), and phase (the phase of this state). The syntax is

State.property


or

st_1.T  # Gets the temperature
st_1.p  # Gets the pressure
st_1.v  # Gets the specific volume
st_1.u  # Gets the internal energy
st_1.h  # Gets the enthalpy
st_1.s  # Gets the entropy
st_1.x  # Gets the quality
st_1.cp  # Gets the specific heat at constant pressure
st_1.cv  # Gets the specific heat at constant volume
st_1.phase  # Gets the phase at this state


Note

Capitalization is important! The temperature has upper case T, while the other properties are lower case to indicate that they are mass-specific quantities.

[10]:

print('T_1 = {}'.format(st_1.T))
print('p_1 = {}'.format(st_1.p))
print('v_1 = {}'.format(st_1.v))
print('u_1 = {}'.format(st_1.u))
print('h_1 = {}'.format(st_1.h))
print('s_1 = {}'.format(st_1.s))
print('x_1 = {}'.format(st_1.x))
print('cp_1 = {}'.format(st_1.cp))
print('cv_1 = {}'.format(st_1.cv))
print('phase_1 = {}'.format(st_1.phase))

T_1 = 400.0 kelvin
p_1 = 101324.99999999953 pascal
v_1 = 1.801983936953226 meter ** 3 / kilogram
u_1 = 2547715.3635084038 joule / kilogram
h_1 = 2730301.3859201893 joule / kilogram
s_1 = 7496.2021523754065 joule / kelvin / kilogram
x_1 = None
cp_1 = 2009.2902478486988 joule / kelvin / kilogram
cv_1 = 1509.1482452129906 joule / kelvin / kilogram
phase_1 = gas


In this case, the value for the quality is the special Python value None. This is because at 400 K and 101325 Pa, the state of water is a superheated vapor and the quality is undefined except in the vapor dome. To access states in the vapor dome, we cannot use T and p as independent properties, because they are not independent inside the vapor dome. Instead, we have to use the pairs involving the other properties (possibly including the quality) to set the state. When we define the quality, the units are dimensionless or percent. For instance:

[11]:

T_2 = Q_(100.0, 'degC')
x_2 = Q_(0.1, 'dimensionless')
st_2 = State('water', T=T_2, x=x_2)
print('T_2 = {}'.format(st_2.T))
print('p_2 = {}'.format(st_2.p))
print('v_2 = {}'.format(st_2.v))
print('u_2 = {}'.format(st_2.u))
print('h_2 = {}'.format(st_2.h))
print('s_2 = {}'.format(st_2.s))
print('x_2 = {}'.format(st_2.x))

T_2 = 373.15 kelvin
p_2 = 101417.99665788244 pascal
v_2 = 0.16811572834411825 meter ** 3 / kilogram
u_2 = 627756.5746698529 joule / kilogram
h_2 = 644806.535045544 joule / kilogram
s_2 = 1911.9019425021506 joule / kelvin / kilogram
x_2 = 0.1 dimensionless


In addition, whether you use the 'dimensionless' “units” for the quality as above, or use the 'percent' “units”, the result is exactly equivalent. The next cell should print True to the screen to demonstrate this.

[12]:

x_2 == Q_(10.0, 'percent')

[12]:

True


From these results, we can see that the units of the units of the properties stored in the State are always SI units - Kelvin, Pascal, m3/kg, J/kg, and J/(kg-Kelvin). We can use the to function to convert the units to anything we want, provided the dimensions are compatible. The syntax is State.property.to('units').

[13]:

print(st_2.T.to('degF'))
print(st_2.s.to('BTU/(lb*degR)'))

212.00000039999995 degF
0.4566499337207774 btu / degR / pound


Note

The values are always converted in the State to SI units, no matter what the input units are. Therefore, if you want EE units as an output, you have to convert.

If we try to convert to a unit with incompatible dimensions, Pint will raise a DimenstionalityError exception.

Warning

If you get a DimensionalityError, examine your conversion very closely. The error message will tell you why the dimensions are incompatible!

[14]:

print(st_2.T.to('joule'))

---------------------------------------------------------------------------
DimensionalityError                       Traceback (most recent call last)
<ipython-input-14-9725ac474279> in <module>
----> 1 print(st_2.T.to('joule'))

DimensionalityError: Cannot convert from 'kelvin' ([temperature]) to 'joule' ([length] ** 2 * [mass] / [time] ** 2)


Here we have tried to convert from 'kelvin' to 'joule' and the error message which is the last line says

DimensionalityError: Cannot convert from 'kelvin' ([temperature]) to 'joule' ([length] ** 2 * [mass] / [time] ** 2)


The dimensions of a temperature are, well, temperature. The formula for energy (Joule) is $$m*a*d$$ (mass times acceleration times distance), and in terms of dimensions, $$M*L/T^2*L = L^2*M/T^2$$ (where in dimensions, capital $$T$$ is time). Clearly, these dimensions are incompatible. A more subtle case might be trying to convert energy to power (again, not allowed):

[15]:

Q_(1000.0, 'joule').to('watt')

---------------------------------------------------------------------------
DimensionalityError                       Traceback (most recent call last)
<ipython-input-15-352febbe91fd> in <module>
----> 1 Q_(1000.0, 'joule').to('watt')

DimensionalityError: Cannot convert from 'joule' ([length] ** 2 * [mass] / [time] ** 2) to 'watt' ([length] ** 2 * [mass] / [time] ** 3)


## Other Common Errors¶

Other common errors generated from using ThermoState will raise StateErrors. These errors may be due to

1. Not specifying enough properties to fix the state, or specifying too many properties to fix the state
2. Specifying a pair of properties that are not independent at the desired condtions
3. Entering an unsupported pair of property inputs (the currently unsupported pairs are Tu, Th, and us, due to limitations in CoolProp)
4. Specifying a Quantity with incorrect dimensions for the property input

An example demonstrating #4 from above:

[16]:

State('water', v=Q_(1000.0, 'degC'), p=Q_(1.0, 'bar'))

---------------------------------------------------------------------------
StateError                                Traceback (most recent call last)
<ipython-input-16-95363eb6e667> in <module>
----> 1 State('water', v=Q_(1000.0, 'degC'), p=Q_(1.0, 'bar'))

StateError: The dimensions for v must be [length] ** 3 / [mass]


## Summary¶

In summary, we need to use two (2) independent and intensive properties to fix the state of any simple compressible system. We need to define these quantities with units using Pint, and then use them to set the conditions of a State. Then, we can access the other properties of the State by using the attributes.

[17]:

h_3 = Q_(2000.0, 'kJ/kg')
s_3 = Q_(3.10, 'kJ/(kg*K)')
st_3 = State('water', h=h_3, s=s_3)
print('T_3 = {}'.format(st_3.T))
print('p_3 = {}'.format(st_3.p))
print('v_3 = {}'.format(st_3.v))
print('u_3 = {}'.format(st_3.u))
print('h_3 = {}'.format(st_3.h))
print('s_3 = {}'.format(st_3.s))
print('x_3 = {}'.format(st_3.x))

T_3 = 666.0536816976213 kelvin
p_3 = 669560197.2594368 pascal
v_3 = 0.0010136928689306822 meter ** 3 / kilogram
u_3 = 1321271.6027173032 joule / kilogram
h_3 = 1999999.9999990154 joule / kilogram
s_3 = 3100.0000000000005 joule / kelvin / kilogram
x_3 = None