# State equation

The first is the state equation and the latter is the output equation if the function f ( ⋅ , ⋅ , ⋅ ) {\displaystyle f(\cdot ,\cdot ,\cdot )} is a linear combination of states and inputs then the equations can be written in matrix notation like above. The equation called the thermic equation of state allows the expression of pressure in terms of volume and temperature p = p(v, t) and the definition of an elementary work δa = pδv at an infinitesimal change of system volume δv.

A simple example of the equation of state for gases is the clapeyron-mendeleev equation pν = rt, where r is the gas constant and v is the volume of one mole.

What is an equation of state (eos) an eos is the relation between functions of state, such as temperature (t), pressure (p), volume (v), internal energy or specific heat it characterizes the state of matter of a material under a given set of physical conditions eoss are used to describe gases. Equation of state: equation of state, any of a class of equations that relate the values of pressure, volume, and temperature of a given substance in thermodynamic equilibrium the simplest known example of an equation of state is the one relating the pressure p, the volume v, and the absolute temperature t of one. Digital electronics: introduction to state table, state diagram & state equation contribute: website .

Key concept: defining a state space representation a n th order linear physical system can be represented using a state space approach as a single first order matrix differential equation: the first equation is called the state equation and it has a first order derivative of the state variable(s) on the left, and the state variable(s) and input(s), multiplied by matrices, on the right. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions it is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature , pressure , volume , or internal energy. The equation of state can be written in terms of the specific volume or in terms of the air density as p v = r t p = r r t notice that the equation of state given here applies only to an ideal gas, or a real gas that behaves like an ideal gas there are in fact many different forms for the equation of state for different gases.

Engineers use a slightly different form of the equation of state that is specialized for a particular gas if we divide both sides of the general equation by the mass of the gas, the volume becomes the specific volume, which is the inverse of the gas density. This feature is not available right now please try again later.

## State equation

The first equation shows that the system state change is dependent on the previous system state, the initial state of the system, the time, and the system inputs the second equation shows that the system output is dependent on the current system state, the system input, and the current time. In a state space system, the internal state of the system is explicitly accounted for by an equation known as the state equation the system output is given in terms of a combination of the current system state, and the current system input, through the output equation.

• State variables the internal state variables are the smallest possible subset of system variables that can represent the entire state of the system at any given time the minimum number of state variables required to represent a given system, , is usually equal to the order of the system's defining differential equationif the system is represented in transfer function form, the minimum.

The simplest known example of an equation of state is the one relating the pressure p, the volume v, and the absolute temperature t of one mole of a perfect gas that is, pv = rt, in which r is the universal gas constant dense real gases, liquids, and solids have more complicated equations of state. State equations for dynamic circuits consider a dynamic circuit that does not contain any • loops consisting entirely of capacitors and voltage sources. The equation of state is a mathematical expression that interrelates the parameters of state characterising the thermodynamic system at a given instant of time examples of parameters of state are: pressure (p), volume of the system (v), its temperature (t) and its internal energy (u.

State equation
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