# Isentropic Process Explanation Essay

**What is adiabatic process?**

When few systems are subjectedtocertain processes where they are thermally insulated without utilizing the heat transferring procedure, that process is known as anadiabatic process.

**Defining reversible process**

Quantity of transferred heat entropy change of system

This equation directly defines the meaning of reversible process.

**Explaining Reversible adiabatic process**

A process that follows both the above procedures (adiabatic and reversible) is known as areversible adiabatic process. This process is isentropic in nature.

**Explanation inrelation with thermodynamics**

A reversible adiabatic process is stated to be isentropic in nature.Anisentropic process is explained to be adiabatic,and the complete work transfer is frictionless in a system. This process is reversible as matter or heat does not transfer in this process.

**Polytropic process**

In this process, there is involvement of both work and heat. During the proceedings in case of polytropic processes, computation of heat transfer is mainly based on 2 aspects.

**#1**

Evaluation of work through steady and open flow process

**#2**

Assessment of work for closed process with the help of,

Between both, any of the ones can be used.

**Reversible Adiabatic Process: procedure to detect the governing equation**

In thermodynamics, an **isentropic process** is an idealized thermodynamic process that is both adiabatic and reversible.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]} The work transfers of the system are frictionless, and there is no transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes.^{[7]}

The word 'isentropic' is occasionally, though not customarily, interpreted in another way, reading it as if its meaning were deducible from its etymology. This is contrary to its original and customarily used definition. In this occasional reading, it means a process in which the entropy of the system remains unchanged, for example because work done on the system includes friction internal to the system, and heat is withdrawn from the system, in just the right amount to compensate for the internal friction, so as to leave the entropy unchanged.^{[8]}

## Background[edit]

The 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 refers to a reversible process, which is an imagined idealized theoretical limit, never actually occurring in physical reality.^{[9]}^{[10]} For an isentropic process, which by definition is reversible, there is no transfer of energy as heat because the process is adiabatic. In an irreversible process of transfer of energy as work, entropy is produced within the system; consequently, in order to maintain constant entropy within the system, energy must be removed from the system as heat during the process.

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, thus the conjugate process would be an isothermal process in which the system is thermally "connected" to a constant-temperature heat bath.

## Isentropic processes in thermodynamic systems[edit]

The entropy of a given mass does not change during a process that is internally reversible and adiabatic. A process during which the entropy remains constant is called an isentropic process, written or . ^{[11]} Some examples of theoretically isentropic thermodynamic devices are pumps, gas compressors, turbines, nozzles, and diffusers.

### Isentropic efficiencies of steady-flow devices in thermodynamic systems[edit]

Most steady-flow devices operate under adiabatic conditions, and the ideal process for these devices is the isentropic process.The parameter that describes how efficiently a device approximates a corresponding isentropic device is called isentropic or adiabatic efficiency.^{[12]}

Isentropic efficiency of Turbines:

Isentropic efficiency of Compressors

Isentropic efficiency of Nozzles

For all the above equations:

- is the specific enthalpy at the entrance state
- is the specific enthalpy at the exit state for the actual process
- is the specific enthalpy at the exit state for the isentropic process

### Isentropic devices in thermodynamic cycles[edit]

Ideal Rankine Cycle 1->2 Isentropic compression in a pump

Ideal Rankine Cycle 3->4 Isentropic expansion in a turbine

Ideal Carnot Cycle 2->3 Isentropic expansion

Ideal Carnot Cycle 4->1 Isentropic compression

Ideal Otto Cycle 1->2 Isentropic compression

Ideal Otto Cycle 3->4 Isentropic expansion

Ideal Diesel Cycle 1->2 Isentropic compression

Ideal Diesel Cycle 3->4 Isentropic expansion

Ideal Brayton Cycle 1->2 Isentropic compression in a compressor

Ideal Brayton Cycle 3->4 Isentropic expansion in a turbine

Ideal Vapor-compression refrigeration Cycle 1->2 Isentropic compression in a compressor

NOTE: The isentropic assumptions are only applicable with ideal cycles. Real cycles have inherent losses due to compressor and turbine inefficiencies and the second law of thermodynamics. Real systems are not truly isentropic, but isentropic behavior is an adequate approximation for many calculation purposes.

## Isentropic flow[edit]

In fluid dynamics, an **isentropic flow** is a fluid flow that is both adiabatic and reversible. That is, no heat is added to the flow, and no energy transformations 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.

Note that energy **can** be exchanged with the flow in an isentropic transformation, as long as it doesn't happen as heat exchange. An example of such an exchange would be an isentropic expansion or compression that entails work done on or by the flow.

For an isentropic flow, entropy density can vary between different streamlines. If the entropy density is the same everywhere, then the flow is said to be homentropic.

### Derivation of the isentropic relations[edit]

For a closed system, the total change in energy of a system is the sum of the work done and the heat added,

The reversible work done on a system by changing the volume is,

where is the pressure and is the volume. The change in enthalpy () is given by,

Then for a process that is both reversible and adiabatic (i.e. no heat transfer occurs), , and so . All reversible adiabatic processes are isentropic. This leads to two important observations,

- , and

Next, a great deal can be computed for isentropic processes of an ideal gas. For any transformation of an ideal gas, it is always true that

- , and .

Using the general results derived above for and , then

- , and
- .

So for an ideal gas, the heat capacity ratio 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 for an ideal gas, ,

- proof:
- as nR= constant itself so we can divide both sides by "nR" and still have constant term in the R.H.S.
- Ultimate result,

also, for constant (per mole),

- and

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