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In thermodynamics
Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
, an isentropic process or isoentropic process (iso = "equal" (Greek); entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 = "disorder") is one during which the entropy of the system remains constant. It can be proved that any reversible
Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy....
 adiabatic process
Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid....
 is an isentropic process.

e is the amount of energy the system gains by heating, is the temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of the system, and is the change in entropy.






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In thermodynamics
Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
, an isentropic process or isoentropic process (iso = "equal" (Greek); entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 = "disorder") is one during which the entropy of the system remains constant. It can be proved that any reversible
Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy....
 adiabatic process
Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid....
 is an isentropic process.

Background


Second law of thermodynamics
Second law of thermodynamics

The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in Thermodynamic equilibrium will tend to increase over time, approaching a maximum value at equilibrium....
 states that, where is the amount of energy the system gains by heating, is the temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of the system, and is the change in entropy. The equal sign will hold for a reversible process
Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy....
. For a reversible isentropic process, there is no transfer of heat energy and therefore the process is also adiabatic
Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid....
. For an irreversible process, the entropy will increase. Hence removal of heat from the system (cooling) is necessary to maintain a constant internal entropy for an irreversible process so as to make it isentropic. Thus an irreversible isentropic process is not adiabatic.

For reversible processes, an isentropic transformation is carried out by thermally "insulating" the system from its surroundings. Temperature is the thermodynamic conjugate variable
Conjugate variables (thermodynamics)

In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature/entropy or pressure/volume....
 to entropy, and so the conjugate process would be an isothermal process in which the system is thermally "connected" to a constant-temperature heat bath.

Isentropic flow


An isentropic flow is a flow
Flow

Flow may refer to:In science and technology:*Dataflow, computing term related to the flow of messages between software components*Environmental flow, the amount of water necessary in a watercourse to maintain a healthy ecosystem...
 that is both adiabatic and reversible. That is, no energy is added to the flow, and no energy losses occur due to friction
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 or dissipative effects
Dissipation

In physics, dissipation embodies the concept of a dynamical system where important mechanical modes, such as waves or oscillations, lose energy over time, typically due to the action of friction or turbulence....
. For an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline.

Derivation of the isentropic relations


For a closed system, the total change in energy of a system is the sum of the work done and the heat added,
The work done on a system by changing the volume is, where is the pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 and the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
. The change in enthalpy
Enthalpy

In thermodynamics and chemistry, the enthalpy is a quotient or description of thermodynamic potential of a system, which can be used to calculate the heat transfer during a quasistatic process taking place in a closed system thermodynamic system under constant pressure....
  is given by,

Since a reversible process is adiabatic (i.e. no heat transfer occurs), so . This leads to two important observations,
, and


or


=>


The heat capacity ratio
Heat capacity ratio

The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume ....
 can be written as,

For an ideal gas is constant. Hence on integrating the above equation, assuming a perfect gas, we get
i.e.




Using the equation of state
Equation of state

In physics and thermodynamics, an equation of state is a relation between thermodynamic variables. More specifically, an equation of state is a thermodynamic equations describing the state of matter under a given set of physical conditions....
 for an ideal gas, ,




also, for constant (per mole),
and






Thus for insentropic processes with an ideal gas,
or


Table of isentropic relations for an ideal gas




Derived from:







Where: = Pressure = Volume = Ratio of specific heats = = Temperature = Mass = Gas constant for the specific gas = = Universal gas constant = Molecular weight of the specific gas = Density = Specific heat at constant pressure = Specific heat at constant volume

See also

  • Adiabatic process
    Adiabatic process

    In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid....
  • Isenthalpic process
    Isenthalpic process

    An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, H; or Enthalpy#Specific enthalpy, h....
  • Polytropic process
    Polytropic process

    A polytropic process is a thermodynamic process that obeys the relation:,where P is the pressure, V is volume, n is any real number , and C is a constant....