## What are the thermodynamics state variables?

In the dynamical system, there is a set of variables, and one of the variables that are used to describe the mathematical state is known as a state variable. In the absence of any external forces, the state of the system describes as much as required about the system to determine its future behavior affecting the system.

The state variable is a system of thermodynamics where every equilibrium state is completely described by a specific value of some macroscopic variables.

A thermodynamics system is not always in equilibrium. In short, thermodynamic state variables describe the equilibrium state of a system. There are two kinds of thermodynamic state variables: extensive and intensive. Extensive variables specify the 'Size' of the system whereas intensive variables such as pressure and temperature do not. To report which variable is extensive and which intensive, think of a relevant system in equilibrium.

The system is divided into two equal parts; the variables that remain unchanged for each part are intensive. The variables whose value gets half in each part are extensive. It is easy to understand, for example, that internal energy(U), volume(V), and total mass (M) are extensive variables. Pressure(P), and temperature(T) are intensive variables. In equation: ∆Q= ∆U+P∆V

Example

###### thermodynamics state variables

An equilibrium state of a gas is completely specified by the value of pressure, volume, temperature, and mass.

Another example is when thermodynamics is not always in equilibrium if gas is allowed to expand freely against a vacuum as shown in the above figure(a). During the rapid expansion, the pressure of the gas may not be uniform throughout. In the same way mixture of petrol vapor and air when ignited by a spark is not an equilibrium state again its pressure and temperature are not the same as shown in the above figure(b).

In a mechanical system, it is possible to find the future state of the objects in the system, the position coordinates, and velocities of mechanical parts are typical state variables.

State function depends on the independent state variables. Like the internal energy, temperature, heat, and work are not state functions, but process functions.

The population size of the plant, animal, and resources are typical state variables in the ecosystem models.

Some more examples of the state variables are:

Internal energy

Enthalpy

Entropy

Volume

Pressure

Temperature

## Control System engineering

In the area of science and engineering and control engineering, the state of a general system is represented by the use of state variables. state-space of the system is the set of possible combinations of state variable values.

State equation is the past states and most recent input the equations relating to the current state of a system and the equations expressing the values of the output variables in form of the input and state variables are known as the output equations.

Discrete-time system: The state vector (vector of state variables) representing this state of a discrete-time system (i.e. digital system) is x[n], wherever n is the distinct purpose in time at which the system is being evaluated. The discrete-time state equations square measure

Continuous-time system: The state vector representing the present state of a continuous-time system (i.e. analog system) is x(t), and also the continuous-time state equations give the evolution of the state vector area unit.

State-space representation: If the space is linear, time-invariant, and finite-dimensional, then the differential and mathematics equations are additionally written in matrix kind. The state-space technique is defined by a very important algebraization of general system theory that produces it achievable to use mathematician vector-matrix structures. the potential of these structures could also be efficiently applied to analysis systems with modulation or whereas not. The state-space illustration (also known as the "time-domain approach") provides a convenient and compact method to model and analyze systems with multiple inputs and outputs.

## What is the thermodynamics equation of state?

The state of matter under pressure, temperature, volume, or internal energy is the equation of state which means it relates to the state variables. In the Helmholtz free energy, most modern equations of state are formulated. Equations of state are used to narrate the properties of a pure substance and mixtures in liquid, gas, and solid-state as well as the state of matter. In other words, it is the relation between state variables. It is a thermodynamics equation describing the state of matter under a given set of physical conditions. The equation of state is further classified into different equations: cubic equation of state, virial equation of state, physically-based equation of state, and many more. The general equation of state is written in this form: f(p, V, T)= 0 where p is the pressure, V= volume, and T is the temperature. And other state variables may be used in this form. It is related to the Gibbs phase rule, which means the number of independent variables depends on the number of substances in the system.

An equation of state correlates densities of gasses and liquids to temperature and pressure, this is called the ideal gas law. Ideal gas law further classifies into the classical ideal gas law may be written as pV= nRT. And another one is the Quantum ideal gas law. In this, the equation of state for elementary particles with mass m and spin takes into account quantum effects.

###### equation of state

## Cubic and virial equation of state

Cubic functions can be rewritten as the cubic equation of state as Vm. Van der Waals equation of state is the origin of the cubic equation of state. So all the cubic equations can be known as the modified van der Waals equation of state. In 1949, the Redlich-Kwong equation of state was introduced. It is a considerable improvement over other equations of the time and this comes under the cubic equation of state. Due to its relatively simple form, It is still of interest primarily. It performs poorly concerning the liquid phase While superior to the van der Waals equation of state, so it cannot be used for accurately calculating vapor-liquid equilibria. Therefore, with separate liquid-phase correlations for this purpose, it can be used in conjunction.

The virial equation is very important as it can be obtained from statistical mechanics. This equation is also known as the Kamerlingh One's equation. Theoretical expressions can be developed for each of the coefficients If appropriate assumptions are made about the mathematical form of intermolecular forces. The first viral coefficient is A, which has a constant value of 1 and makes the statement that when the volume is large, all fluids behave like ideal gasses. B is the second virial coefficient corresponding to interactions between pairs of molecules, C to triplets, and so on. There is an increase in accuracy by considering higher-order terms indefinitely. The functions of temperature coefficients B, C, D, etc.

## List of the further equation of state

Stiffened equation of state:Is often used: p=p(y-1)e-yp0, Where e is the internal energy, y is an empirically describe constant and p0 is another constant molecular

Ultrarelativistic equation of state

Ideal bose equation of state

JWL(Jones -Wilkins -Lee) equation of state

Tait equation of state

Murnaghan equation of state

Birch-Murnaghan equation of state

Stacey Brennan Irvine equation of state

Modified Rydberg equation of state

An adapted polynomial equation of state

Johnson Holmquist equation of state

Mie gruneisen equation of state

## Conclusion

The state variable is a system of thermodynamics where every equilibrium state is completely described by a specific value of some macroscopic variables. In equation: ∆Q= ∆U+P∆V. The connection between the state variables is called the equation of state. Thermodynamics is not always in equilibrium if gas allows expansion freely. State variables include internal energy, volume, temperature, and pressure. In the equation of state, there are many equations given by different scientific research with their name, and a list of equations of State is also understood above. State equation is the past states and most recent input the equations relating to the current state of a system and the equations expressing the values of the output variables in form of the input and state variables are known as the output equations. Equations of state are used to narrate the properties of a pure substance and mixtures in liquid, gas, and solid-state as well as the state of matter. In other words, it is the relation between state variables.