What is a state?
 
 
 
 

Thermodynamic 
systems.
 
 
 

Local Thermodynamic
Equilibrium or LTE.
 
 
 
 
 
 

A local state is a set of attributes that describe the LTE.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

State as an image - an analogy.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  Volume vs. surface state.
 
 
 
 
 
 
 

In thermodynamics we deal with systems, which are defined as anything (e.g. a block of copper, a piston-cylinder device, a nozzle, a combustion chamber, an entire power plant etc.) with a clearly defined boundary. 

The working material within the system may be stationary and uniform (a block of copper at rest) or dynamic and non-uniform (a steam turbine). However if you imagine a local neighborhood  at a point - (well, not quite a point but, say, a micron sized cube)- at a given instant (again, not quite an instant but, say,  a microsecond duration), there are are still so many billions of molecules and so many trillions of collisions (or other means of energy exchange),  that a dynamic (force balance), thermal  (temperature balance) and chemical  (chemical balance) equilibriums are almost instantly established in that neighborhood. Under this triple equilibrium, also known as the local thermodynamic equilibrium or LTE., the properties  (observable characteristicssuch as the temperature or pressure) of the local system assume stable values that would not change with time were the local system instantly isolated from its surroundings.

The LTE, at a given point at a given time can be characterized by a set of attributes or properties which is called a thermodynamic state .  The list of state variables (p, T, rho, v, u, h, s, V,  etc.) that comprise a state can be quite long and may depend on the working substance, velocity and location of the observer, and even the system configuration. Evaluating a  state amounts to determining the associated state variables. Fortunately not all the state variables are independent, they are related by the equations of state making the task of state evaluation a little easier. For two states to be identical the two sets of state variables must be identical. If even one of the properties between two states are different, the states are different.

Before we start with a few concrete examples, let us draw a familiar analogy. Suppose the computer screen is a thermodynamic system where the color and brightness of each pixel is determined through  local thermodynamic equilibrium. In that case a pixel represents a little local neighborhood or the local system, and the color and brightness attributes of the pixel are the state variables. Other state variables may include the red, green, blue or gray levels, not all of which are independent and can be inferred from the color relations (equations of state). Just like an image occupying the entire screen is made up of states of  individual pixels, the state of a large system at a given instant can be expressed as an ensemble of its local states at that instant. Carrying this analogy further, we can imagine a state camera analogous to a digital camera capable of capturing the state of a system. Instead of recording the intensity of red, green and blue colors, it records the set of variables that describes the LTE at each little neighborhood. The state image captured by a state camera of a block of copper at a uniform temperature can be quite dull (a single state everywhere similar to a blue screen of death for a PC screen), while that of the turbine startup will be quite colorful with the image rapidly evolving to a complex pattern as the turbine revs up. 

We will revisit this analogy time and time again when discussing different types of systems in later chapters. 

b. Volume and Surface States: When we evaluate a state, say, at a turbine inlet, we evaluate the state at the inlet port at a given instant. It is assumed that the state   does not vary across the cross-section.  Such states are called a surface state in TEST. Similarly, when we say that a gas in a piston-cylinder device is at a particular state , it is assumed that the system is uniform so that a single state describes the entire system. This is called a volume state.

Classification of Properties

Six classes of
working substance.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Fig. 2.1 A typical thermodynamic plot (T-v) showing a number of states in different regions. 

c. State Properties: Not all  state attributes are of equal significance. A property is a state variable that does not depend on the history of the system. If a state of a local system at an instant is know, the properties there will have unique values irrespective of what this system has gone through up to this moment.

Some properties , such as molecular mass, critical temperature, enthalpy of formation etc., depend on the nature of the working substance and do not change with location or time in a given system. Such properties are intrinsic to the material of the working substance and are called Material Properties. An important material property is the molecular mass, MM , defined as the mass of a kmol (or pound mole) of the material, a kmol (or lbmol) being a standard number (Avogadro Number) of molecules chemists prefer to use to count the multitude of molecules or atoms just as a dozen is preferred for counting eggs in a super market. The total amount of matter can be expressed through mass m or the number of kmols n=m/MM .

Properties such as temperature T , static pressure p , specific volume v , density rho , internal energy u , enthalpy h , entropy s etc., are  independent of the frame of reference. The velocity or location of the observer will not change the value of such properties intrinsic to the thermodynamic state. They are called the thermodynamic properties and are tabulated in thermodynamic tables found at the appendices of most textbooks.  The best way to measure thermodynamic properties is to move with the flow, if any, at the location of interest so that there is no dynamic effect. Some of the properties are derived from others:  rho=1/v and h=u+pv are thermodynamic  relations which are always true.

There are quite a few dynamic properties, such as the velocity,  the kinetic energy, the dynamic pressure etc., that depend on the velocity of the observer. There are others such as the potential energy that depend on the location of the reference point or datum. They are called the extrinsic properties . The velocity Vel , height z from a common reference point called the datum, specific kinetic energy k.e.=Vel^2/2 , specific potential energy p.e.=gz , specific total energy e=u+ke+pe , and specific total enthalpy j=u+ke+pe   are examples of extrinsic properties.

There are some other variables, such as the total mass m , volume Vol , area of cross section A of a pipe, or the mass flow rate mdot=rho*A*Vel , which depend on the state as well as system configuration. They are called the System Properties .  Some of the system properties appear as part of the state daemon in TEST. 

Sometime the same variable can be classified in different ways depending on how a working fluid is modeled. Density for instance, can be a material property for a solid and a thermodynamic property for a gas. The extrinsic properties e and j  reduce to thermodynamic properties u and h if the kinetic and potential energy changes are negligible in a problem.

Another way to classify the state variables is to consider if the attributes are additive or not. Variables such as temperature, pressure, velocity, density etc., which are not cumulative in nature are called intensive variables, while variables such as mass, volume, internal energy, enthalpy, entropy etc. are additive and are called extensive. If an overall system represented by a single state is divided into any number of sub-systems, the temperature, an intensive variable, is identical between the overall system and the individual sub-systems, while the volume, an extensive variable, of the overall system is the sum of the volumes of the sub-systems. 

It is customary in thermodynamics to express the total amount of an extensive variable with capitalized symbols, Vol, U , H, S etc., and to reserve the lower-case letters for intensive properties p , x, y  etc. The notable exceptions are temperature T, the total mass m,  and the total number of moles n . When the extensive properties are expressed on unit mass basis (for instance, kJ/kg for energy) - v (=V/m), u(=U/m ), h(= H/m) , and s (= S/m)  for example - they are called specific properties .  If expressed on the basis of unit mole (kJ/kmol for energy) , they are called molal specific properties . The generic symbol phi is used to represent any specific properties. Other symbols adopted are Vel for velocity, ke (= Vel ^2 ) for specific kinetic energy and pe (=gz , z being the height of a local system from a standard datum) for specific potential energy, KE (=m * Vel^2 ) for total kinetic energy and PE (=mgz ) for total potential energy.
 

Phase-Changer?
 
 
 
 
 

Ideal-Gas?
 
 
 
 
 
 
 
 

Perfect-Gas?
 
 
 
 
 
 
 
 
 

Real-Gas?
 
 
 
 
 
 
 
 
 
 
 
 

Solid or Liquid?
 
 
 
 
 
 

Mixture?
 
 
 
 
 
 
 
 
 

One fluid, many models!

If the working substance is not a solid, treat the fluid as phase-changer,  provided  saturation and superheated tables are available (TEST : Material must be listed in the phase-changer database). 

If the working fluid is gaseous and no phase-change tables are available, start with the ideal gas model. For T>2T_cr or p<0.01p_cr, this model yields quite reasonable results. Because  cv and cp are temperature dependent, you may still need ideal gas tables or functional correlation between cp and T , and material property M to determine the specific properties  (TEST: The particular gas must be listed in the ideal gas database).

If the gas happens to be a noble gas (He, Ar, Ne etc.) or the temperature variation in the problem of interest is not large, use the perfect gas model. All the ideal gas assumptions are retained for a perfect gas; moreover, cv and cp are constant producing simpler formulas for the evaluation of specific properties. You will need the material property cp and M to determine the specific properties  (TEST: If a particular gas is not in database, you can create a custom gas by specifying the material properties).

If the ideal gas assumptions breaks down because T<2T_cr and/or p>0.01p_cr, and there are no phase-change tables available, try the real gas model as the last resort. This is quite an universal model capable of handling  gas, vapor, liquid-vapor mixture and even liquid phase. Of course, such generality comes at the expense of accuracy. The critical properties, the generalized compressibility chart and the enthalpy and entropy departure charts must be available to apply the real gas model (TEST: The particular gas must be listed in the real gas database).

If the phase of the working substance is consistently a solid or a liquid with no possibility of a phase change, the solid/liquid model is applicable.  You will need the material properties rho and c to determine the specific properties  (TEST: If a particular solid or liquid is not available, you can create a custom solid or liquid by specifying the material properties).

If the working substance has multiple chemical components, it still can be treated as a pure substance, a mixture ,  provided the components belong to a single category above. If chemically different components from different categories are mixed, say liquid nitrogen (real gas or phase-change model) and gaseous oxygen ( ideal gas or perfect gas), the resulting mixture is not a pure substance , a prerequisite for classical thermodynamic treatment.

f. What Model to Choose? Sometime a working fluid can fall under different categories. For instance H2O can be found in the Solid/Liquid, Ideal Gas, Perfect Gas, Real Gas and Phase-Change categories. Unless there is any particular reason for using a specific model, use the following order in choosing a model: phase-changer, soild/liquid, perfect gas, ideal gas, real gas, mixture. The simplest model for liquid water in a pumping problem is the solid/liquid model. However, if the possibility of a phase change exists (pumping saturated water for instance), a phase-change model would be much more accurate. Water vapor in moist air can be treated as a perfect gas without any lack of accuracy. The ideal gas model is suitable in combustion problems because the temperature variation can be significantly large. The real gas model, despite its lack of accuracy, can be very useful in regions not covered by the phase change tables and for fluids for which tables are not available.

The next panel, called the Global-Control Panel,  contains a few global control buttons, which will be discussed later. The radio buttons Mixed and SI , and  English allow used of any combination of units,  the System International (often, mistakenly, referred to as the Metric system) or the English system. Units can be changed at any time during a problem solving session.

The lower part of the state panel gives a definition of the extended state used in TEST. The main body consists of a group of widgets representing state variables such as pressure, temperature etc. Notice that the symbols, p, T, x etc., are followed by a numeric suffix, the state number. If you choose a different state, say, State-2, from the State Choice (next to the Calculate button) of the Local-Control Panel , the suffix after the symbols changes to 2 globally. 

Suppose we would like  to evaluate the enthalpy, h ,  of steam at a pressure of 100 kPa and a quality of 0.5. 

Note that every variable-widget has four components: a checkbox, the variable symbol with the state suffix, a value field and a unit choice. On the primary window choose a state, say, State-1 from the State Choice. Click the p1-box to turn on the p-widget . The background color of the variable-widget becomes lighter (your monitor must be set to display 32-bit color), the variable symbol changes font (p1 to  p1), the unit changes color (kPa to kPa ) and the background of the value field becomes yellow with the cursor appropriately positioned for you to type in a value. If you turn-off (by un-checking the box) the p-widget , it goes back to its original format. Now turn on the  p-widget and x-widget (do not bother to enter the values at this point). Now try turning on the T-widget . The daemon does not allow you to do so (with appropriate message on the Message Panel ) because one cannot independently specify pressure, quality and temperature of a two-phase mixture. 

Now enter pressure by clicking on the value (yellow) field to position the insertion cursor and then typing in the value 100   for p1   (you do not need to hit 'Enter'). To enter quality as a fraction, type in .5 and change the  unit from % to fraction by choosing the desired unit from the Unit Choice.

The desired variable, enthalpy h, is shown to have a value of 1546.36 kJ/kg.  To express it in another unit, say, cal/g, simply choose the desired unit from the unit choice and the unit conversion is done on-the-fly producing a value of 396.325 cal/g for h. If you click on the English radio-button, the entire state is converted to english system. Now go back to SI units by clicking the SI button.

Now, suppose instead of known p and x, p and h are supplied for the same state and we are to determine x. Simply turn-off x and click on the h-checkbox. The value of h remains unaltered (you do not have to type it in again). Calculate the state to find x to be 50%, the expected result. Now suppose h and s are supplied instead. As you Calculate the state following the same procedure x is evaluated as 50% and the pressure as 100.025 kPa. The 0.025% error in p is an acceptable price to pay considering how laborious it is to manually evaluate p from a given pair of h and s (you do not even know whether to start at the superheated table or the saturation table).

You can use any valid algebraic expression using the following syntax. Start all expressions with the = sign. To use a state variable in an expression, the symbols used in the daemons must be respected (pressure at state 5, for instance, must be expressed as p5, not pressure5 or P5). Examples of valid expressions are: = p3 , = h+p*v , = h + p *v , =200 , =p3*Vol3^1.4/ p2 , =(h2-h1)/(h3-h1) . 

Suppose we are interested in a third state, isentropic to state-2 at a pressure 10 times that of state-1. Choose State-3 from the state selector, enter p3 as =10*p1 and  s3 as =s2 , and Calculate . 

Calculated states are automatically saved in a stack and can be recovered by simply choosing the state number from the State Choice . The calculated states can also be shown on a variety of thermodynamic plots such as T-s , h-s , p-v etc. Simply choose the desired plot from the Diagram Choice situated next to the State Choice in the local control panel (see Fig. 2 below).
 

There is a reason why different colors are used to display the  Variable Symbols  in the State Panel .  The first group of variables,  p through s, are the Thermodynamic Properties (in blue), which do not depend on the velocity or position of the observer. Variables Vel through j , are evaluated relative to the frame of reference and are called the Extrinsic Properties (in green) , useful for engineering problem solving. The third group of variables, displayed in black, depends on the system configuration (such as volume or area of cross section etc.) and are called the System Properties (in black). Variables Vel and z have a default value of  zero in most daemons, which can be changed by turning the variable widget off and then back on. Some state daemons, such as the ideal gas state daemon, contain state variables (such as molecular mass) that are intrinsic to the material and are called the Material Properties (in red) .

It produces a detailed printer friendly output on the Instructions/Output window. By copying the content of this window (see Fig. 4) to any word processor, one can print or record the details of the calculations. 

It also produces a table of properties (for the calculated staetes) that can be copied into any spreadsheet for further processing. 

And, finally, a few lines of TEST-Codes are produced that can be used to instantly reproduce the visual solution at a later session. For more information, read theo TEST-Codes section in this Tutorial. 

Because all the variables are visually exposed, any coceivable combination of variables can be changed in a parametric study. The working fluid can be changed in a similar manner. Just choose a different fluid from the fluid selector and Super-Calculate the entire solution.

The Super-Iterate button is used in rare situations, whereby states are related in such convoluted manner that further iterations are necessary after the use of the Super-Calculate button. The Super-Initialize button initializes all the calculated states so that one can start all over.  The Load button is for loading TEST-Codes for regenerating an existing solution. It is quite useful for sharing solutions in a peer group. Also if the working fluid model is to be changed (for instance, treating R-134a as a real gas vs. a phase-change fluie), the TEST-Code can transport the solution without having to enter all the input variables all over again.