Joule Thomson effect: An overview

The Joule-Tompson effect is one such topic that is always relevant. We revisit this topic frequently in an attempt to get more clarity. Several of the priceless lessons from the JT effect can be found in this note.?

Joule – Thompson effect is an interplay of heat, work, and internal energy at constant enthalpy.

The Joule-Thomson effect, also known as the Joule-Kelvin effect, is a thermodynamic phenomenon that occurs when a real gas undergoes a throttling process, or expansion, without the addition or removal of heat and work. This effect has significant practical applications in various engineering fields, including refrigeration, natural gas processing, and cryogenics.

The key point is Joule-Thomson effect is an isenthalpic process. The joule-Thomson effect exemplifies the principle of energy conservation, particularly when considering the constancy of internal energy (U) and work (W) while keeping enthalpy constant. This articulates the fundamental concept of conserving energy during adiabatic expansion, and the implication that the internal energy and work within the system remain unaltered. By acknowledging the Joule-Thomson effect as a representation of the preservation of energy and the constancy of enthalpy, it underscores the crucial role of this principle in thermodynamics and its implications for real-world engineering applications.

JT effect exemplifies the behavior of real gases during expansion. Unlike ideal gases, real gases do not always behave predictably when subjected to changes in pressure and temperature. The Joule-Thomson effect helps engineers understand how real gases will behave under different conditions, allowing them to design more efficient and effective systems. As said above, JT is an isenthalpic process. The JT effect is an outstanding thermodynamic principle that provides a deep understanding of the isenthalpic process. It is a fascinating phenomenon where a gas undergoes adiabatic expansion or throttling, meaning there is no heat transfer to the surroundings and also there is no work transfer. Instead, the change in internal energy occurs at the expense of the thermodynamic PV work.

The most important point is the constancy of internal energy (U) and work (W) while keeping enthalpy constant. In JT expansion the sum of U+W remains constant.

Furthermore, although the JT effect is an adiabatic process, it is not isentropic due to internal irreversibilities such as friction. This distinction is crucial in understanding the intricacies of the process and its practical applications in various engineering fields.

?Additionally, the JT coefficient plays a crucial role in understanding the effect. This coefficient describes how the temperature of a gas changes when it undergoes expansion. The inversion temperature is another important concept in the JT effect. This temperature represents the point at which a gas transitions from exhibiting a cooling effect to a heating effect during expansion.

Finally, it is important to consider the exceptions to the JT effect, particularly in the case of certain gases such as hydrogen, helium, and neon. These gases do not exhibit the same behavior as other gases when subjected to the JT effect.

What is the Joule-Thomson effect?

In thermodynamics, the JT effect describes the temperature change of a real gas or liquid when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. This procedure is called a throttling process or JT process. At room temperature, all gases except hydrogen, helium, and neon cool upon expansion by the JT process. Under similar conditions, there is an increase in temperature for H2, He, and Ne.

It is important to study the cooling produced in the JT expansion in refrigeration and also in the petrochemical industry, where the cooling effect is used to liquefy gases. It is also used in many cryogenic applications.

Fundamentals

Real gas vs ideal gas

This is fundamental to the JT effect

Image credit: Google

The deviation of real gas from ideal gas behavior occurs due to the assumption that if pressure increases the volume decreases. The volume will approach a smaller number but will not be zero because the molecules will occupy some space that cannot be compressed further. It has been observed, at high pressure, the measured volume of the gas is more than the calculated volume. But at low pressure, the calculated and the measured volumes approach each other. So, it can be

stated that the real gases do not follow Boyle’s law perfectly under all conditions of temperature and pressure.

Hence, the volume of the gas molecules for real gases is a significant fraction of the volume of the container at higher pressure.

When we use the ideal gas law, we make a couple of assumptions:

-We ignore the volume taken up by the imaginary ideal gas molecules

-We ignore that the gas molecules do attract or repel each other

However, we know that in real life, gases are made up of atoms and molecules that take up some finite volume, and we also know that atoms and molecules interact with each other through intermolecular forces. One way we can look at how accurately the ideal gas law describes our system is by comparing the molar volume of real gas with the molar volume of an ideal gas.

Let n be the number of moles, V is the volume of real gas, the molar volume of real gas = V/n

Refer to the ideal gas equation, PV = n RT. The molar volume = RT/P

The ratio of the molar volume of real gas / molar volume of ideal gas = V/n / RT/P = PV/n RT

This ratio is called compressibility of gas and is expressed by the symbol Z

Z = PV/ n RT

Z = 1 for ideal gases

Compressibility factor Z for gases: Very important concept for JT expansion

Thus, the compressibility factor of gas tells us how far the gas is from ideal behavior and this has a huge meaning in cryogenics.

There are two factors [1] high pressure and [2] low temperature that make a real gas deviate from ideal behavior PV = n RT

Effect of pressure on the gas compressibility: Contributes to excluded volume

Pressure brings molecular repulsive forces into dominance

?Image credit: Google

This graph shows the compression factor?Z?over a range of pressures for many gases. For all of the real gases [ every gas is a real gas] in this graph, you might notice that the shapes of the curves look a little different for each gas, and most of the curves only approximately resemble the ideal gas line at?Z equals 1?over a limited pressure range. Also, for all the real gases?Z?is sometimes less than?1 at very low pressures, which tells us that the molar volume of real gases is less than that of an ideal gas. As you increase the pressure past a certain point that depends on the gas,?Z?gets increasingly larger than?1. That means, at high pressures, the?molar volume of real gases is larger than?the ideal gas.

The next question that automatically arises is, why?

At high pressures, the gas molecules get more crowded and the amount of space between the molecules is reduced. This makes the repulsive forces coming to dominance tend to make the volume larger than for an ideal gas; when these forces dominate Z is greater than unity.

The error in molar volume gets worse the more compressed the gas becomes, which is why the difference between?Z?for the real and ideal gas increases with pressure.

Effect of temperature on the compressibility of gases:?Contributes to intermolecular forces.

Image credit: Google

At low temperatures the attractive forces dominate

You may notice that the compressibility of N2 [the molar volume of real gas / ideal gas volume ratio] of N2 is less than 1 stands for an ideal gas at -100 degc. This ratio goes near 1 at 25 degc and then shoots up with Z > 1 at 600 degc. You would also notice that at high pressure the Z value of N2 is >1 at all temperatures.

What does it mean?

Explanation

The pressure we measure comes from the force of the gas molecules arising from the kinetic energy of the molecules at that temperature hitting the walls of the container. At a relatively larger temperature, a gas molecule has more kinetic energy to overcome the intermolecular attractions and hit the wall giving more P and consequently also more V because of the larger spread of molecules. This results in a much larger positive deviation of real gases with a bigger positive Z > 1 at high temperatures.?This reverses at low temperature and low pressure the condition that applies to the JT effect. The intermolecular forces become much more prominent at low temperatures because

the molecules have less kinetic energy to overcome the intermolecular attractions. The molecules come closer. The compressibility reduces mostly Z <1.?Here, the attractive forces dominate. The relative importance of attractive forces decreases as temperature increases.

The van der Waals [VDW] equation

The van der Waals [VDW] equation is the simplest equation to model the behavior of real gases. VDW equation corrects the ideal gas equation of state PV = n RT by including the effect of gas molecule volume and intermolecular forces.

?The fundamental equation for ideal gases is PV = n RT

Let us assume P is pressure and V is the volume of an ideal gas

The van der Waals equation corrects for two properties of real gases: the excluded volume of gas particles and attractive forces between gas molecules.

The van der Waals equation is presented as:

(P+an2/V2) (V?nb) = n RT

P, equals?measured pressure

V, equals?the volume of the container

n, equals?moles of gas

R, equals?gas constant

T, equals?temperature (in Kelvin)

Compared to the ideal gas law, the VdW equation includes a “correction” to the pressure term, [?an^2/V^2] which accounts for the measured pressure being lower due to attraction between gas molecules. The “correction” to the volume, [?nb ] subtracts out the volume of the gas molecules from the total volume of the container to get a more accurate measure of the empty space available for the gas molecules.?a and?b are measured constants for a specific gas (and they might have some slight temperature and pressure dependence).

At low temperatures and low pressure, the correction for volume is not as important as the one for pressure, so?Z?is less than?1. At high pressures, the correction for the volume of the molecules becomes more important so?Z?is greater than?1. At some range of intermediate pressure, the two corrections cancel out and the gas appears to follow the relationship given by the ideal gas.

?JT effect: How does it work?

Mechanism of JT effect

JT effect is approximated as an Isenthalpic process. It’s an interplay of heat, work, and internal energy at constant enthalpy.

How is JT isenthalpic?

It is an experimental fact that JT is an isenthalpic process backed by thermodynamics.

?What is ‘isenthalpic’

A process becomes isenthalpic when there is no change in the enthalpy of the process. The constancy of enthalpy means the sum of internal energy, U and work, W remains constant.

How JT is unique

There are many adiabatic processes while generally, in most of them, ?dQ = 0 but there is adiabatic work transfer to surroundings. Let’s look at two common adiabatic processes [1] compressors and [2] turbines in power plants. While both are adiabatic processes, they do transfer ‘work’ to their surroundings. Compressors transfer adiabatic work to isothermal interstage coolers and the turbine transfers adiabatic work to condenser.

JT is unique. It retains the ‘work’ within the system and uses the internal energy to perform the work that causes cooling in JT effect.

From the first law of thermodynamics,

H = U + PV

where U is internal energy, P is pressure, and V is volume. the change in PV represents the work done

The net work is done when a mass m of the gas expands

W = mV1P1 - m V2P2

as the gas expands from P1VI to P2V2, it does a W amount of work.

From the first law of thermodynamics dU = delta Q – delta W

In the JT process, delta Q=0 as the process is adiabatic

dU = - delta W

mU2-mU1 = - mP2V2 + mP1V1

mU2 + mP2V2 = mU1 + mP1V1

This gives mH1 = mH2,

H1=H2 meaning Isenthalpic process.

In summary, the JT effect contains heat and work within the system. The ‘work ‘consumes internal energy at constant enthalpy that does the cooling.

Joule Thomson coefficient μ and inversion temperature [ An important concept]

The rate of change of temperature T concerning pressure P in a Joule–Thomson process (that is, at constant enthalpy H) is the Joule–Thomson (Kelvin) coefficient

This coefficient can be expressed in terms of the gas's volume V, its heat capacity at constant pressure Cp, and its coefficient of thermal expansion alpha as

μ = dT/dP = V/Cp [ alpha x T – 1]

The Joule–Thomson coefficient of an ideal gas is zero. In real gases, the Joule–Thomson coefficient is different from zero and depends on pressure and temperature. For μ JT > 0, temperature decreases, and for μ JT < 0, temperature increases during an expansion.

The temperature at which the sign of the Joule–Thomson coefficient changes is the inversion temperature, which itself depends on pressure. The inversion temperature of most gases is above ambient temperature, but for hydrogen, the inversion temperature is about T = ? 80 °C. The values for the Joule–Thomson coefficient help to realize the changes occurring during processes.

Inversion temperature and compressibility of a gas is central to JT effect

The inversion temperature and JT coefficient are related subjects. This has been discussed together above.??Few more lines about inversion temperature. Some of them may be the repetition of what is already said above.

The inversion temperature in thermodynamics and cryogenics is the temperature below which a non-ideal gas (all gases in reality) that is expanding at constant enthalpy will experience a temperature decrease, and above which will experience a temperature increase. This temperature change is known as the Joule–Thomson effect, Helium, hydrogen, and Neon are three gases whose Joule–Thomson inversion temperatures at a pressure of one atmosphere are very low (e.g., about 45 K, ?228 °C for helium). Thus, these gases warm when expanded at constant enthalpy at typical room temperatures. On the other hand, nitrogen, and oxygen, the two most abundant gases in the air, have inversion temperatures of 621 K (348 °C) and 764 K (491 °C) respectively: these gases can be cooled from room temperature by the Joule–Thomson effect.

Image credit: Google

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H2, He and Ne don’t cool by JT expansion

All real gases except H2, He, and Ne cool, when expanded at constant enthalpy below, their inversion temperature. For example, the N2 gas has an inversion temperature of 621 k, much above the normal ambient temperature. Those gases that cool are represented by the positive JT coefficient and those that don’t by the negative JT coefficient.

All real gases those which have Z<1, have molar volume < ideal gas. They have intermolecular attraction.?When they expand their KE slows down because they have to expand against

?

attractive forces. Reduction in KE reduces temperature. PE gains energy. Total internal energy = KE + PE remains constant.

H2 is an exception [ HE and Ne are the other two exceptions]

The inversion temperature of H2 gas is 200 k much below the ambient temperature [ image below]. When H2 is expanded at room temperature the gas becomes hot instead of cooling. But H2 does show a JT effect if it is expanded below 200k.

Explanation:

What triggers this temperature change behind the scenes is intermolecular attractions and repulsions.

All molecules have some attractions and repulsions working between them. This arises because the electrons are moving around the nucleus continuously and this movement is unevenly distributed and changing continuously. When at some point there is more electron density at a particular location, that particular point acquires a negative charge, and another end becomes positively charged to balance it. These are called temporary dipoles.

?The opposite charge ends produce attraction and similar charge ends produce repulsion when the molecules come closer. Unless a molecule is ionic in nature there is a balance of the positive and negative charges.

What difference is made that makes H2 cool if expanded <200k and heat up if expanded at 298 k, the ambient temperature?

At 200k H2 has relatively less kinetic energy, molecules are closer and molecules have relatively more intermolecular attractions compared to 298 K [ambient temperature] that H2 exploits for its cooling below its inversion temperature.?On the contrary, at 298K [ambient temperature] H2 molecules have more kinetic energy, more collisions, more pressure, and more repulsion, Z > 1, see the image.

?Image credit: Google

??The compressibility Z of H2 further increases when H2 is expanded because of lack of intermolecular attractions Its volume becomes even larger than ideal gas. This gas expansion needs more translational kinetic energy which is supplied by the potential energy. This kinetic energy sends molecules farther apart adding KE to the gas that heats H2.

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