| Thermodynamics |
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A polytropic process is a thermodynamic process that obeys the relation:
where p is the pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer.
Some specific values of n correspond to particular cases:
In addition, when the ideal gas law applies:
Where is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume ().
For an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy the process is polytropic, such that
where C is a constant, , , and with the polytropic coefficient .
For certain values of the polytropic index, the process will be synonymous with other common processes. Some examples of the effects of varying index values are given in the following table.
| Polytropic index | Relation | Effects |
|---|---|---|
| n < 0 | — | Negative exponents reflect a process where work and heat flow simultaneously in or out of the system. In the absence of forces except pressure, such a spontaneous process is not allowed by the second law of thermodynamics [ citation needed ]; however, negative exponents can be meaningful in some special cases not dominated by thermal interactions, such as in the processes of certain plasmas in astrophysics, [1] or if there are other forms of energy (e.g. chemical energy) involved during the process (e.g. explosion). |
| n = 0 | Equivalent to an isobaric process (constant pressure) | |
| n = 1 | Equivalent to an isothermal process (constant temperature), under the assumption of ideal gas law, since then . | |
| 1 < n < γ | — | Under the assumption of ideal gas law, heat and work flows go in opposite directions (K > 0), such as in vapor compression refrigeration during compression, where the elevated vapour temperature resulting from the work done by the compressor on the vapour leads to some heat loss from the vapour to the cooler surroundings. |
| n = γ | — | Equivalent to an isentropic process (adiabatic and reversible, no heat transfer), under the assumption of ideal gas law. |
| γ < n < ∞ | — | Under the assumption of ideal gas law, heat and work flows go in the same direction (K < 0), such as in an internal combustion engine during the power stroke, where heat is lost from the hot combustion products, through the cylinder walls, to the cooler surroundings, at the same time as those hot combustion products push on the piston. |
| n = +∞ | Equivalent to an isochoric process (constant volume) |
When the index n is between any two of the former values (0, 1, γ, or ∞), it means that the polytropic curve will cut through (be bounded by) the curves of the two bounding indices.
For an ideal gas, 1 < γ < 5/3, since by Mayer's relation
A solution to the Lane–Emden equation using a polytropic fluid is known as a polytrope.
In thermodynamics, an adiabatic process is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. As a key concept in thermodynamics, the adiabatic process supports the theory that explains the first law of thermodynamics.
The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This is in contrast to igniting the fuel-air mixture with a spark plug as in the Otto cycle (four-stroke/petrol) engine. Diesel engines are used in aircraft, automobiles, power generation, diesel–electric locomotives, and both surface ships and submarines.
In thermodynamics, the specific heat capacity of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity or as the specific heat. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
In thermodynamics and fluid mechanics, the compressibility is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure change. In its simple form, the compressibility may be expressed as
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
In astrophysics, a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature T of a system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange (see quasi-equilibrium). In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).
In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed, inelastic container: The thermodynamic process is the addition or removal of heat; the isolation of the contents of the container establishes the closed system; and the inability of the container to deform imposes the constant-volume condition.
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: ΔP = 0. The heat transferred to the system does work, but also changes the internal energy (U) of the system. This article uses the physics sign convention for work, where positive work is work done by the system. Using this convention, by the first law of thermodynamics,
A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor.
The bulk modulus of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume. It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas or κ (kappa), the isentropic exponent for a real gas. The symbol γ is used by aerospace and chemical engineers.
A thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. If at every point in the cycle the system is in thermodynamic equilibrium, the cycle is reversible. Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function.
The Lenoir cycle is an idealized thermodynamic cycle often used to model a pulse jet engine. It is based on the operation of an engine patented by Jean Joseph Etienne Lenoir in 1860. This engine is often thought of as the first commercially produced internal combustion engine. The absence of any compression process in the design leads to lower thermal efficiency than the more well known Otto cycle and Diesel cycle.
Fanno flow is the adiabatic flow through a constant area duct where the effect of friction is considered. Compressibility effects often come into consideration, although the Fanno flow model certainly also applies to incompressible flow. For this model, the duct area remains constant, the flow is assumed to be steady and one-dimensional, and no mass is added within the duct. The Fanno flow model is considered an irreversible process due to viscous effects. The viscous friction causes the flow properties to change along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with uniform properties over any cross section of the duct.
The Cauchy number (Ca) is a dimensionless number in continuum mechanics used in the study of compressible flows. It is named after the French mathematician Augustin Louis Cauchy. When the compressibility is important the elastic forces must be considered along with inertial forces for dynamic similarity. Thus, the Cauchy Number is defined as the ratio between inertial and the compressibility force in a flow and can be expressed as
Isentropic nozzle flow describes the movement of a gas or fluid through a narrowing opening without an increase or decrease in entropy.
