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Isentropic Process and Isentropic Efficiency

Updated: Nov 5, 2023

What is an isentropic process?

The process during which entropy remains constant is called an isentropic process.

In a world where everyone says the entropy of the universe keeps on increasing, having an isentropic process seems to be a misnomer and in fact it is.

The isentropic process is an ideal concept in thermodynamics and it serves as a model for devices with minimal irreversibilities and near-perfect insulation. That means the process that has the least amount of frictional losses internally and the near-perfect insulation at the thermodynamic boundary of the device resulting in negligible heat transfer between surroundings and system. In these rare cases, isentropic process approximation works well for designing systems.

What causes entropy to increase?

Entropy is changed either by Irreversibilities or Heat Transfer over a finite temperature difference.

More the irreversibility (like friction) in the system, the more will be the increase of entropy during the process. Similarly, whenever there is the transfer of heat over a finite temperature difference there must be a rise in entropy.

On the other hand, the process which is internally reversible and adiabatic is isentropic.

Reversible Adiabatic Device
Device undergoing Isentropic Process

But the converse is not true. All the isentropic processes need not always be reversible adiabatic. As explained in the example below, the process can be irreversible and non-adiabatic and still be isentropic.

Irreversible and non adiabatic Isentropic process
Special case of isentropic process

What kind of devices undergo (Ideally) an isentropic process?

Steady flow devices like Nozzles, Turbines, Pumps, Compressors, Diffusers.

How to show an isentropic process on an h-s diagram?

On the enthalpy-entropy diagram, the isentropic line is vertical from S1 to S2 for work producing devices like Turbines or in the reverse direction in case of work consuming devices like refrigeration systems or heat pumps.

Isentropic process line on h-s diagram
Isentropic process on h-s plot

For the Isentropic process, entropy change during the process is zero because S1=S2.

entropy change in the isentropic process is zero.

But in nature, no process is isentropic and there is always a presence of irreversibilities and heat transfer over finite temperature difference which cause the entropy to increase.

Irreversible process on h-s Plot
Actual process on h-s plot

Note: Irreversible processes should always be drawn as dotted lines on the property plots

For real-world processes entropy of the system and the universe always increases.

Change in Entropy

Some processes do result in a decrease in entropy but they increase the entropy somewhere else in the system/surroundings resulting in the net increase of entropy of the universe.

Once one understands that there is no machine or device that is perfect in nature, he can compare it to the perfect device or process so that he can understand where the performance can be improved. One of the ways of comparison is the calculation of Isentropic efficiency.

Isentropic efficiency

To find out how much the irreversible process deviates from the ideal isentropic process the isentropic efficiency is calculated for steady flow devices.

This is similar to comparing the performance of the actual given cycle with the Carnot cycle which is an idealized thermodynamic cycle and has the highest performance (thermal efficiency, work output, etc)

In a similar way, the performance of a steady flow device is compared to an isentropic process which is an idealized thermodynamic process.

More isentropic efficiency means a better design of the system. The calculation procedure of isentropic efficiency varies according to the type of device. (Turbine, Pump, Compressor, etc)

This is a little tricky because it is somewhat confusing at the first time but if one understands the concept of work consuming and work producing devices and what is expected from them then it becomes easier.

Isentropic Efficiency for Work Producing Devices (Turbines)

For work producing devices, actual work produced is always less than isentropic work(ideal).

Again, the isentropic process is just an idea and is not possible in nature.

Before calculating isentropic efficiency, we should know how to calculate the work for steady flow devices. Usually, it is a difference between enthalpy values at the inlet and exit of the device.

Isentropic process and enthalpy values at state points.
Isentropic process on T-s plot

In this case, the isentropic work Ws is nothing but the difference between h1 and h2s.

Isentropic Work

How to find specific enthalpy(h) values at state points?

There are two different cases based on working fluid in the system.

1. Specific enthalpy value for the ideal gas is nothing but the product of specific heat capacity and temperature at that state. h=CpT

2. For systems using pure substances(water, refrigerants) as working fluids the enthalpy values need to be taken from property tables(steam tables, refrigerant property tables).

Now that we have enthalpy values we can learn more about the actual processes that happen in reality. In the actual process, the enthalpy at the exit is always more than the isentropic value as shown below.

Irreversible process T-s plot
Actual process T-s plot

Actual work Wa is given by,

Irreversible work output turbine

Actual work produced from work-producing devices like turbines is always less than the isentropic work. Isentropic efficiency is nothing but the ratio of Actual work Wa to Isentropic work Ws.

Isentropic efficiency of work producing device
Isentropic efficiency of work producing device

A well-designed turbine can have isentropic efficiency as high as 90%.

Isentropic Efficiency for Work Consuming Devices(Pumps/Compressor)

Now we will see the isentropic efficiency of work consuming devices like pumps and compressors. These devices do not produce any thermodynamic work by themselves but we need to provide the energy from outside. Usually, energy is provided to them from the electricity grid or stand-alone prime movers like diesel engines or sometimes batteries.

Hence, we should remember that these devices require energy from outside to perform compression or pumping of the fluid.

The actual compression processes and final state is shown below.

Difference between adiabatic reversible process and irreversible process
Difference between Isentropic process and actual process on h-s plot

Actual work required from work-consuming devices is always less than the isentropic work. Isentropic efficiency of the compressor/pump is nothing but the ratio of Isentropic work Ws to Actual work Wa.

Real process on T-s Diagram
Real process on T-s Diagram

Isentropic efficiency of work consuming device
Isentropic efficiency of work consuming device

Now that we have learned what is an isentropic process and what isentropic efficiency is, we as engineers and scientists should always strive to increase the isentropic efficiency which means reducing the irreversibilities in the system and making near-perfect insulation to avoid heat losses. Although we can improve the isentropic efficiency we would never reach 100% efficiency as reality is always different than ideal processes and concepts.

I would like to end this article by quoting physicist Arnold Sommerfeld,

“Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you anymore.” - Arnold Sommerfeld
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