# isentropic

In thermodynamics, an isentropic process (iso = "same" (Greek); entropy = "disorder") is one during which the entropy of the system remains constant.

## Background

Second law of thermodynamics states that,
where is the amount of energy the system gains by heating, is the temperature of the system, and is the change in entropy. The equal sign will hold for a reversible process. For a reversible isentropic process, there is no transfer of heat energy and therefore the process is also adiabatic. For an irreversible adiabatic 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. 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 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 that is both adiabatic and reversible, that is no energy is added to the flow, and no energy losses occur due to friction or dissipative effects. 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 pressure is,
where being the pressure and the specific volume. The change in enthalpy () 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 can be written as,

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

Using the equation of state for an ideal gas, ,
Thermodynamics (from the Greek θερμη, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on
Ice melting - a classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.
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 equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
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Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable (from a dia bainein), corresponding here to an absence of heat transfer.
conjugate variables such as pressure/volume or temperature/entropy. In fact all thermodynamic potentials are expressed in terms of conjugate pairs.

For a mechanical system, a small increment of energy is the product of a force times a small displacement.
An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to
Flow may refer to:
• Flow (physics) is the flux times the area. This is the rate at which something travels through a given cross section.

Friction is the force of two surfaces in contact. It is not a fundamental force, as it is derived from electromagnetic forces between atoms. When contacting surfaces move relative to each other, the friction between the two objects converts kinetic energy into thermal energy, or
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.
Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.

Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.