# Thermodynamic system

thermodynamic system is a defined quantity of matter, or a defined portion of space (geometrically delimited). This system is delimited by surfaces (or walls or boundaries), also known as control surfaces; everything that is external to the system, and is able to interact with it, is called an environment.

The control surface of a thermodynamic system represents the boundaries of the thermodynamic system and characterizes it according to its intrinsic properties of interaction between the system and the environment; in fact, depending on the type of control surface we will have closed, open or isolated thermodynamic systems. The boundary of a thermodynamic system can be classified with three essential parameters: permeability, rigidity and thermicity.

• Permeability: the boundary of the control surface may not allow a flow of matter (mass) or porous, that is, allow a flow of matter, even selectively.
• Rigidity: the boundary of the control surface can be rigid not allowing changes in volume (and therefore also in work), or mobile allowing changes in volume (and therefore also in work).
• Thermicity: the boundary of the control surface can be adiabatic, that is, it does not allow heat exchange, or diathermic, that is, it allows heat exchange.

The thermodynamic state of a thermodynamic system is defined as the set of values assumed by those measurable thermophysical properties, or by the physical quantities that characterize it, such as pressure, volume, entropy, temperature and so on. The properties thus characterized are defined quantities or state parameters, because of the correspondence between the values assumed and the state identified. It should be noted that this formulation configures a state of macroscopic character, in the sense that it is identified by values of the quantities deriving from the average on a large number of particles, and can, in fact, correspond to infinite distributions of positions and speeds at the microscopic level.

A thermodynamic state is in equilibrium if the parameters that define the thermodynamic state are stationary or independent of time. You can vary the parameters that define the state, that is, the state variables, in many ways. If the variation of the state variables and therefore of the state itself leads from one state of equilibrium to another state of equilibrium it is said that a thermodynamic transformation has occurred. The graphical representation of the set of thermodynamic states that a system can assume when varying some thermodynamic quantities (for example temperature, pressure, volume, and composition) takes place through state diagrams.

## Types of thermodynamic system

Based on the type and combination of properties of the control surfaces, the following types of thermodynamic system can be distinguished:

• open system: its boundaries are permeable, albeit partially, to the passage of matter;
• closed system: it is delimited by boundaries impermeable to the passage of matter; in other words, a closed system cannot exchange matter with the environment, but only energy;
• isolated system: a system is said to be isolated when, in addition to being closed, it does not exchange energy with the external environment.

The thermodynamic systems listed above are nothing more than a combination of these properties:

• open system: porous, mobile, and diathermic;
• adiabatic open system: porous, movable and adiabatic;
• closed system: impervious, mobile and diathermic;
• adiabatic closed system: impervious, movable and adiabatic;
• isolated system: impervious, rigid and adiabatic.

It is clear, from these definitions, that a closed system is characterized by the constancy of its mass, while the opposite is not true, in the sense that a system with constant mass is not necessarily closed: in fact, it could also be an open system in permanent regime, that is a system in which, instant by instant, the incoming mass is perfectly equal to the outgoing one.

## Intensive and extensive properties of a thermodynamic system

Each characteristic of a thermodynamic system is called property; the properties of a system are divided into:

• intensive properties: these are those that do not depend on the size of the system, for example: temperature, pressure, density (if a system is large, or small, it does not influence the temperature, pressure or density of the system);
• extensive properties: these are those that depend on the size, or extent, of the system, for example: mass, volume, total energy (if a system is large, or small, it influences the mass, the volume and the total energy of the same, as the mass will be larger, or smaller, the volume will be larger, or smaller, the total energy contained will be larger or smaller).

A state variable is extensive if its value depends on the mass of the system; these variables are also called additive because their total value can be obtained as the sum (or integral) of the values of the various parts of the system.

A variable is intensive if its value is a local function of a particular point of the system. For example, pressure is an intensive variable: it can be different in every point of the system, its total value in the system is not obtained by summing the value of the pressures in the various parts. On the contrary, volume is an extensive variable: it is not locally definable, and if we divide the system into parts the total volume is the sum of the partial volumes.

For each extensional variable it is possible to define a corresponding specific (or more properly mass) variable, i.e. the ratio of the variable in question to the mass of the system. Generally, the extensional variables are indicated with a capital letter, the corresponding specific variables with the corresponding lower case letter. As a first example, the volume of the system is indicated with V, and is measured in m3; the corresponding specific variable (specific volume) is indicated with v = V/M, is measured in m3/kg, and represents the volume of the mass unit.

## Thermodynamic transformation of a system

It takes the name of thermodynamic transformation (or thermodynamic process) of a system, any modification which involves the variation of at least one of its internal properties. Depending on whether this variation is infinitesimal or finite we will have an infinitesimal or finite transformation.

It is necessary to distinguish a transformation from a simple physical phenomenon: for example, a simple system consisting of a fluid which changes its position in space without other consequences, represents a physical phenomenon, but certainly not a transformation: in fact, if the fluid changes its position, probably changes its potential energy (related to quota), but this is an external properties of the system. The same applies if the system under examination changes shape but remains unchanged in volume. A particular transformation is the so-called cycle: it is a finite transformation that brings the system back to the same state from which it started.

### Energy transfers: heat and work

The energy that, during any transformation, crosses the surfaces of the system is given the name of heat or work: we speak of heat when the energy is transferred as a consequence of a temperature difference existing between the system and the environment; otherwise, if the energy flow does not derive from a temperature difference, this is called work.

According to these last definitions, it is possible to talk about heat and work only in presence of an energy flow between the system and the environment; it doesn’t make sense to talk about heat and work for a system that is in a defined thermodynamic state (i.e. are wrong expressions like heat of a system or work of a system). In other words, heat and work are not state properties of the system.

A type of work that is often encountered is related to the displacement of one or more walls of the system as a result of an alteration of the mechanical equilibrium: in this case we speak of (mechanical) work of volume variation and it is obviously equal to the work done by the external forces acting on the walls that move. Let’s take a concrete example: we consider a system consisting of a fluid contained in a cylinder on which a piston is weighted; initially, we assume that the fluid pressure balances the pressure of the external forces (weight force of the piston), so the system is in thermodynamic equilibrium. Suppose now to increase the external weight force by adding weights on the piston: the initial equilibrium undergoes a perturbation and the system undergoes a transformation that brings it in a new state of equilibrium.

During the transformation, there is energy that is transferred from the environment to the system: this energy, assuming no friction, corresponds to the work of the external forces (since there is no difference in temperature, the energy can only be work according to the definitions given above), work that produces a decrease in fluid volume. If, on the contrary, there had been an increase in fluid volume, the work of volume change would have involved a transfer of energy from the system to the environment.

Another important type of work is the one related to the rotation of one or more walls of the system, due to an alteration of the mechanical equilibrium: this type of work is called mechanical work of propeller; it is obtained when, for example, inside a cylinder containing fluid there is a rotating propeller. During the transformation, due to friction between the rotating surfaces and the fluid, there is energy that is transmitted from the environment to the system: this energy, in the absence of mechanical friction, corresponds exactly to the energy used to move the propeller.

An important thing to note is that the propeller work, for a closed system, can involve energy transfer in only one direction, that is from the environment to the system, and never vice versa (it is good to remember that this is valid only for a closed system as we will see that there are special open systems – such as turbines – in which a fluid in motion is used to make the propellers rotate and therefore produce mechanical energy to be converted, subsequently, in other forms of energy). The two examples just examined (work of volume variation and work of propeller) therefore involve an alteration of the mechanical equilibrium of the system. In other cases, the balance that is altered can be, for example, electrical or magnetic: in these cases, in the presence of energy transfer between the environment and the system, we will speak, respectively, of electrical work or magnetic work. An example of electric work is a system consisting of a container containing fluid and a resistance immersed inside, connected with an external electric circuit. When the electric circuit is activated, the current flows through the resistor, which by heating alters the electrical balance, transferring energy from the environment to the system: in fact the resistor heats up, by Joule effect, and gives heat to the fluid (by convection).

It should be noted that, if we consider only the fluid as the system of interest, we cannot speak of work but of heat, because the energy is transmitted, in this case, by temperature difference between the resistor (which now is the environment) and the system and not by electric potential difference. Another observation concerns the fact that the energy transfer, also in this example, can never happen from the system to the environment but only from the environment to the system, since the system contains only purely passive elements. Different would be the case if the system includes a capacitor, which can receive energy when charging and give it when discharging.

### Symbols and sign conventions for work and heat

Heat and work are indicated, respectively, with the symbols Q and W and their metrological dimensions are obviously those of energy: in the International System, they are measured in Joules (symbol: J), while in the Technical System they are measured in kilocalories (symbol: kcal). Furthermore, although heat and work are not state properties, it makes sense to consider the amount of heat exchanged per unit of mass (or weight) of the system and the work done per unit of mass (or weight) of the system. Again, for the energy balances of a system it is always necessary to give a sign to the numerical value of heat and work, depending on the direction of their flow; there are then two different conventions for work and heat:

• heat is positive if energy is administered to the system, while it is negative otherwise;
• work is positive if energy is supplied to the environment, while it is negative otherwise.

### Types of thermodynamic transformations

#### Quasi-static transformation

A quasi-static transformation is defined as a thermodynamic transformation that occurs extremely slowly, so that the thermodynamic system under examination, passing from an initial equilibrium state A to a final equilibrium state B, goes through a succession of infinite equilibrium states, separated by infinitesimal transformations and infinitesimal variations of the system properties. If we want to identify a finite transformation, it is necessary to know, in addition to the initial and final states, all the infinite intermediate states through which the system passes and then all the values that define each state.

Let’s consider a system in thermodynamic equilibrium; if we modify, by an infinitesimal amount, some of the properties of the environment in order to alter the equilibrium between the environment and the system, the system will undergo an infinitesimal transformation that will bring it in a new equilibrium condition. Then, if we realize a finite transformation through a succession of infinitesimal transformations, we obtain a so-called quasi-static transformation: it is therefore characterized by the fact that, in every instant, the system is, unless infinitesimal, in a condition of thermodynamic equilibrium.

Let’s consider a closed system cylinder-piston containing fluid in equilibrium conditions at a certain pressure and temperature; we want to double the fluid pressure while maintaining unchanged the temperature: we can do this by putting the system in contact with a source that is at the same temperature and applying instantly on the piston an adequate weight. In this way, the system is brought to the desired final equilibrium conditions, but through a transformation during which it is never in equilibrium. The transformation is therefore not almost static. We could however proceed in another way: always putting the system in contact with the source that keeps it at constant temperature, we can successively increase the weight applied on the piston of an infinitesimal quantity and wait, at each increase, the reaching of the equilibrium. In this way, the transformation is constituted by a succession of equilibrium states and is therefore almost static: in particular, it is an isothermal transformation. It was not isothermal the previous transformation: in fact, in that case, during the transformation it was not possible to define the thermodynamic state, so it was not possible to talk about internal properties and, in particular, about temperature.

#### Reversible and irreversible transformations

A thermodynamic transformation is defined reversible if it, starting from a state of thermodynamic equilibrium, takes place in such a way that the system and the environment can always be brought back to their respective initial states, going through the same transformation without any trace of it remaining. This definition has two fundamental consequences

• the first is that a reversible transformation goes through a succession of equilibrium states, which means that it is a quasi-static transformation;
• the second is that a reversible transformation can, during the inverse transformation, make the system and the environment pass through the same states encountered in the direct transformation, by means of equal and opposite operations; the mechanical and thermal energy exchanges of the direct transformation are equal and opposite to those of the inverse transformation.

Ultimately, a reversible transformation, once traveled in the two directions, does not result in any change in the system or the environment. To conclude, we emphasize that a reversible transformation is not absolutely feasible in reality, so it is pure abstraction. It is useful, for example, to know the maximum value of the work obtainable in a transformation characterized by positive work or the minimum value for the work to be spent in a transformation with negative work.

An adiabatic transformation is a type of thermodynamic transformation characterized by the fact that the system does not exchange heat with the environment: this means that \(Q_{1,2} = 0\) and therefore that the first principle of thermodynamics assumes the formulation \(\Delta U_{1,2} = W_{1,2}\). According to this relation, the mechanical energy supplied (or subtracted) to the system, in an adiabatic transformation, is entirely found as an increase (or decrease) of internal energy of the system itself.

A quasi-static adiabatic transformation is also representable in the Clapeyron plane, however, its course depends strictly on the equation of state of the system. Physically, an adiabatic transformation can be considered realized in a system bounded by walls that are perfect insulators.

#### Constant volume (isochoric) transformation

A constant-volume transformation (also called isochor) is a type of thermodynamic transformation that can occur in a system bounded by rigid, fixed walls. Clearly, since it results null the work related to volume changes, the first principle assumes the formulation \(\Delta U_{1,2} = Q_{1,2}\), according to which the thermal energy given (or subtracted) to the system is found entirely as an increase (or decrease) of internal energy of the system.

An interesting thing, in a transformation of this type, is the following: in general, the calculation of the heat exchanged in a transformation needs the knowledge of the transformation itself, state by state, and this is possible only if the transformation is quasi-static; on the contrary, when the volume remains constant, the heat exchanged is equal to the variation \(\Delta U_{1,2}\) of the internal energy and therefore its calculation needs only the knowledge of the initial state and the final state.

#### Constant pressure (isobar) transformation

A constant-pressure transformation (also called isobaric) is a type of thermodynamic transformation that can be thought of as being carried out in a piston-cylinder system by keeping the forces acting on the piston unchanged during the transformation.

#### Constant temperature transformation (isotherm)

A constant-temperature transformation (also called an isotherm) is a thermodynamic transformation that is certainly quasi-static and can be thought of as occurring in a piston-cylinder system in thermal equilibrium with a source.