What is Isentropic Compression?

This article deals heavily with entropy. Entropy is not a simple topic, so we highly recommend checking out HVAC School’s Entropy in Refrigeration and Air Conditioning for some background information.

Describing isentropic compression is a daunting endeavor.

We all recognize the term compression, and I’m sure most of us can deduce that isentropic has something to do with entropy. But what exactly does isentropic compression mean? How and when do we see it at work?

I’m not an engineer by any stretch of the imagination, but I’d still like to explain what isentropic compression is and why it matters to HVAC/R techs.

 

The rules of entropy

Before we dive in too deep, let’s get some basic entropy rules out in the open. 

Simply put, entropy is a state of disorder when molecules get more disorganized and spread out. It is different from enthalpy, which measures heat exchange in our HVAC/R systems. We can treat entropy as a measure of wasted energy potential.

Entropy can only increase overall. We see an entropy “decrease” in the refrigeration cycle, but it refers to entropy within the system. When entropy appears to decrease in the system, the overall entropy increases outside the system. Entropy can also theoretically stay the same. However, physical processes like friction will always add a little bit of entropy.

Within the refrigeration cycle, temperature and pressure directly affect the entropy in the system. Rising temperatures will increase the entropy, and increasing pressure will decrease the entropy. Compressors raise the temperature and pressure of the gaseous refrigerant.

It would make sense for entropy to increase when the temperature rises because molecules move more quickly in higher temperatures. If there’s such a rapid temperature increase in the compressor, shouldn’t the entropy skyrocket with it?

No, and here’s why:

Compressors heat the gaseous refrigerant while applying lots of pressure. Adding pressure decreases entropy because it rapidly decreases the gas volume. That gives the gas molecules less space to move around. When the gas molecules have less space to zoom about, there’s less disorder overall.

The entropy changes that occur due to increasing temperature and pressure will ideally cancel each other out during 100% efficient compression.

 

What does isentropic compression mean?

We’ve already established that isentropic has to do with entropy.

Isentropic has the prefix iso-, which means “same.” Basically, isentropic compression is compression in which the entropy stays the same within the system. It does not increase or decrease.

Look at the standard T-S diagram of the refrigeration cycle below.

A T-S diagram of the refrigeration cycle in which the compression stage is highlighted.

You will notice a vertical line during compression. I’ve highlighted it. The temperature (T value) increases, but the entropy (S value) stays the same. That’s what isentropic compression looks like on a graph. You’ll see that vertical line on most T-S diagrams of the refrigeration cycle.

However, that diagram is only theoretical and represents ideal conditions. In reality, the compressor will never be 100% efficient, as I said earlier. Friction and other sources of mechanical inefficiency will always occur and increase entropy as the system performs work.

But that begs the question: if isentropic compression is physically impossible, why should we care about it?

 

Isentropic efficiency

Isentropic compression in HVAC and refrigeration is a pipe dream. I’ll admit that much.

Being the perfect human being is also a pipe dream. It’s human nature to make mistakes on occasion. But does that stop some people from striving for perfection? No!

It may be helpful to think of isentropic compression as a type of “perfection.” Even though isentropic compression may not be physically possible, it can help us set a standard for combatting inefficiency in the compression process.

As we already said, entropy indicates inefficiency. If we want to reduce inefficiency, isentropic compression is a condition that we can aim to emulate as closely as possible. It’s a standard to which we can (and do) measure the efficiency of real compressors. 

To compare the actual compression to isentropic compression, we use an equation for isentropic efficiency. This equation is a ratio that tells you how a compressor’s efficiency compares to isentropic compression. You divide the isentropic compression work by the actual compression work.

We can use enthalpy to calculate the work performed. Using the variable h to represent specific enthalpy, I will show you how to compare isentropic compression to actual compression. In the equation below, h1 represents the specific enthalpy of gas that enters the compressor, h2 represents the specific enthalpy of the gas that exits the compressor, subscript s signifies the isentropic conditions, and subscript r indicates the real conditions.

The formula for determining isentropic efficiency.

Even though you will never see pure isentropic compression in the field, it is an ideal we can strive for as we limit entropy. The closer the ratio above can get to 1, the more efficient a compressor will be.

 

In conclusion, truly isentropic compression is only theoretical, but that doesn’t mean we should disregard it. 

Think about it this way: we don’t stop trying to better ourselves just because perfection is impossible. The same applies to isentropic compression in a world dictated by natural physics. We can strive to make our systems more efficient by making the compression process as close to isentropic as possible.

In other words, those vertical lines on T-S diagrams aren’t real, but they can serve as a standard for comparison.

 

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