# Your quick guide to Isentropic Process: Relations, Flow, Efficiency and Equations

• Isentropic processes are defined as thermodynamic processes with constant entropy
• Isentropic compression/expansions occurs when there is no transfer of heat
• Isentropic efficiency is that ratio of actual work done to the isentropic work output
• Isentropic flow is reversible and adiabatic - no energy exchanges occur

## Isentropic Process

Isentropic process is defined as a thermodynamic process, where the gas or fluid has constant entropy (constant-entropy process). This means that the isentropic process is a specific type of adiabatic process, where there is no transfer of matter or heat.

It is also a reversible adiabatic process. This means that change in Q = 0, and as temperature can’t be 0, the change in entropy has to be 0 – confirming the process is isentropic.

This type of process is very valuable in engineering because it is an idealized process and can be used for comparisons to real processes. You can an in-depth lecture on isentropic processes here:

## Isentropic Relations

There are many different isentropic relations within thermodynamic cycles, including but not limited to:

### Ideal Brayton Cycle

• Isentropic compression inside of a compressor
• Isentropic expansion inside of a turbine

### Ideal Carnot Cycle

• Isentropic compression
• Isentropic expansion

### Ideal Diesel Cycle

• Isentropic compression
• Isentropic expansion

### Ideal Otto Cycle

• Isentropic compression
• Isentropic expansion

### Ideal Rankine Cycle

• Isentropic compression within a pump
• Isentropic expansion within a turbine

## Isentropic Compression – Isentropic Expansion

An isentropic or adiabatic compression/expansion takes place when the compression/expansion of gas occurs with no heat energy flow in or out of the gas. Molecules do not interact and have no volume in an ideal gas. Pressure varies linearly with quantity and temperature, and inversely with volume. The equation that represents this relationship is:

p – absolute pressure of the gas

V – volume

n – amount of substance

R – universal or ideal gas constant equal to the product of the Avogadro constant and the Boltzmann constant

T – absolute temperature

The letter R here denotes that constant known as the universal gas constant that is equal for all gases: R = 8.31 J/mol K.

### Isentropic Expansion in a Gas Turbine

Modern airbreathing jet engines and gas turbine engines follow the Brayton cycle. The Brayton cycle is a thermodynamic cycle that is used for all constant pressure heat engines. It consists of four thermodynamic processes – two isobaric and two isentropic: Isentropic compression – compressor draws in ambient air, where it is pressurized.

Isobaric heat addition – the air that has been compressed is then passed through a combustion chamber. Fuel is burned and the air is heated, this is a constant-pressure process as the chamber is open on both ends to flow in and out.

Isentropic expansion – the pressurized, heated air will then expand in the turbine, giving up its energy.

Isobaric heat rejection – the remaining heat must then be rejected to close out the cycle.

## Isentropic Efficiency of Turbines

The inlet and exit pressures are constant and fixed for an adiabatic turbine that is subject to a steady-flow process. An isentropic process between the inlet and exit pressures is the idealized process for the turbine. The turbine’s desired output is the isentropic work output. Therefore the isentropic efficiency of the turbine is known as the ratio of the isentropic work of the turbine to the actual work, assuming the turbine is subject to an isentropic process between identical exit and inlet pressures.

ηT =  wa/ws

wa – Actual turbine work

ws – Isentropic turbine work

wa and ws can be determined from the turbine’s energy balance. The potential and kinetic energies related to a process through a turbine is usually negligible compared to the process’ enthalpy change. The energy balance can then be written as:

Therefore the isentropic efficiency of a turbine can be shown as:

ηT  (h2a – h1)/(h2s – h1)

H1 – inlet enthalpy

H2a – actual process enthalpy at exit

H2s – isentropic enthalpy at exit

## Isentropic Flow

Isentropic flow is a fluid flow that is reversible and adiabatic. This means that no energy transformations happen due to dissipative effects or friction, and there is also no heat added to the flow. Isentropic flows happen when the change in flow variables is gradual and small, like an ideal flow through any type of nozzle. If the gas’ speed is far slower than the speed of sound of the gas, the velocity of the flow increases and the density stays constant.

As the speed of the flow increases and approaches the speed of sound, there are compressibility effects on the gas that must be taken into account. The density of the gas will vary from one location to the other.

If this flow is compressed very gradually (the area is decreased) and then expanded gradually (the area is increased), the conditions of the flow revert back to their original values. This makes the process reversible. Considering the second law of thermodynamics, a flow that is reversible has constant entropy. This is what engineers class as an isentropic flow, merging the Greek word “iso” and entropy.

However, in an isentropic transformation, energy can be exchanged within the flow as long as it is not heat exchange(if the specific heat capacity remains the same). If the specific heat capacity stays constant, the gas is known to be calorically perfect, if the specific heat capacity is changed, then the gas is known to be calorically imperfect. Air is calorically perfect at low supersonic and subsonic Mach numbers, but if air is subjected to low hypersonic Mach numbers, it becomes calorically imperfect.

Isentropic expansion or compression that occurs on or by the flow is an example of this type of exchange. Entropy density can vary between various streamlines for isentropic flow. If the entropy density is said to be exactly the same throughout, it is called a homentropic flow.

What is your experience with isentropic processes? If you have anything to add or you feel we have left something out, please reach out and let us know with a comment below!

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