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• Published: 04 June 2024

Semi-empirical model for Henry’s law constant of noble gases in molten salts

• Kyoung O. Lee 1 ,
• Wesley C. Williams 1 ,
• Joanna McFarlane 1 ,
• David Kropaczek 1 &
• Dane de Wet 1  

Scientific Reports volume  14 , Article number:  12847 ( 2024 ) Cite this article

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• Chemical engineering
• Materials science
• Physical chemistry
• Thermodynamics

Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.

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Introduction.

This study investigated the partitioning of noble gases between solution in the molten salt liquid phase and the cover gas. Noble gases constitute the largest fraction of volatile fission products, so their ability to move into the gas phase affects the operational performance of molten salt reactors (MSRs) 1 , 2 . Therefore, mass transport of radioactive species produced during nuclear fission is essential to understanding the performance and the control of molten fuel salts in MSRs. Particularly in liquid–gas systems, the mass transfer of noble gases from the liquid to the gaseous phase across the entire loop system must be taken into account to determine the reactivity and other key nuclear reactor performance parameters.

The system under consideration can be defined as a liquid phase in which a noble gas with limited solubility dissolves in a molten salt. The behavior of radioactive species in molten salts within molar salt reactors can be described by a combination of thermochemical equilibrium and transport dynamics that depend on thermophysical properties in well-mixed turbulent flows. For molten salts, under sufficient conditions of temperature above 700 °C, noble gas solubility is temperature dependent. Additionally, the solubility of a gas dissolved liquid generally is associated with both static and dynamic fluid states. Experimentally, the solubility of gas in a liquid is measured under conditions without any flow. For noble gases in particular, it can be assumed that the liquid–gas transition is governed by species stability expressed as Gibbs free energy.

Henry’s law constant describes the equilibrium ratio of liquid-to-vapor concentrations 3 . Therefore, a study of the temperature dependence of Henry’s law constant was performed in which Gibbs free energy data were fit by applying a regression equation using the salt’s surface tension and the atomic size of noble gases. Quantitative analysis by multiple successive regressions achieved results that strongly support this approach. The results compared favorably with Henry’s law constant data collected from historical references for the molten salt mixtures with noble gases. The computed Henry’s law values depend on salt-specific data, such as surface tension, that have been measured only for a few specific molten salt mixtures.

The understanding of the gas–liquid interface is clarified by the two-film theory, which elucidates this phenomenon by utilizing partial pressures and concentrations, where H represents Henry’s law constant.

The two-film theory has been used to analyze liquid–gas mass transport. Figure  1 is a diagram demonstrating the assumed layered interfaces between the gas and liquid phases. The mass transfer process is considered to occur at the interface between the gas film side and the liquid film side. In the figure, \(c_i\) represents the concentration of species in the liquid phase (i.e., dissolved species), whereas \(p_i^*\) corresponds to the partial pressure of species in the gas phase (i.e., bubble behaviors). During the phase transition, a gas film and a liquid film are formed on the surface between liquid and gas. When the gas transitions from liquid to gas, the behavior is dependent on the concentrations at the interface, \(c_i^*\) in the liquid film and \(p_i^*\) in the gas film. The two-film theory is a diffusion-based mechanism that can be used to describe the transport of gaseous masses across a liquid film using Henry’s gas constant. Henry’s gas constant plays a pivotal role in this context, and it is essential to explore the complexity of these mechanisms and to establish a comprehensive understanding of these phenomena.

When the temperature of the system changes, Henry’s constant changes for the equilibrium process and can be described by the Gibbs free energy. In general, Gibbs free energy is a chemical potential that can be used to determine the stable chemical species of systems and their phase behavior. For noble gas behavior, the equilibrium of a system is established through transitions between liquid and gas phases until the lowest energy condition is met. Thus, models based on Gibbs free energy offer essential insight into the conditions necessary for liquid–gas mixing during phase transition processes, describing surface effects and volumetric energies at specific temperatures and pressures. The temperature of the thermodynamic system remains constant during the transition. However, because the solute and solvent have different densities, the total volume of the system changes with the relative amounts of solute and solvent—that is, during a phase change. The entropy change for an equilibrium process can be explained by the Gibbs free energy change (in J/mol), \(\Delta G=\Delta H -T\Delta S\) , where \(\Delta H\) (in J/mol) represents the enthalpy change, \(\Delta S\) (in J/mol  K) denotes the entropy change, and T (in K) stands for the temperature in Kelvin within the system. In this study, we assume that the noble gas phase transition process consists of a temperature-dependent process and a van der Waals radius that has a polarization effect 4 , 5 . For the solute, a noble gas, to spontaneously separate from the solvent, which takes the form of a molten salt, the translational energy of a solute atom must surpass the intermolecular binding forces trapping it in the salt. The enthalpy change of this process is denoted as \(\Delta H\) , and the reaction consistently exhibits an endothermic nature ( \(\Delta H\) > 0), owing to the energy necessary to overcome the interactions among the molecules within the molten salt.

The corrected Henry’s gas constant for a gas within a liquid can be explained through the equilibrium between the Gibbs free energies of two concurrently existing phases. The phase transition is represented by \(A(g) \rightleftharpoons A(l)\) , where A is the concentration of a noble gas and l denotes the gas dissolved in the solution while g indicates the bubbles in the solution. The equilibrium exists between the gas phase and the liquid (dissolved) phase, including during the reverse process. When examining the scenario where a mole of noble gas dissolves in a molten salt fluid at constant temperature, T , the Gibbs free energy equation results in the following:

Note that the corrected Henry’s gas constant, \(K_H\) , is defined as the dimensionless ratio of \(K_H^e\) [mole/(cm 2  atm)] divided by \(K_{H}^0\) [mole/(cm 2  atm)], where \(K_H^e\) corresponds to the experimental data and \(K_{H}^0\) represents the reference value with \(\alpha \) and \(\beta \) as empirical constants . In experimental data where the impact of pressure can be effectively averaged, alterations in the temperature of a system lead to modifications in Henry’s constant. This change is directly connected to variations in Gibbs free energy. Employing the method of least squares regression facilitates the determination of \(\alpha \) and \(\beta \) , which are used to compute the equilibrium constant. The units of \(\alpha \) and \(\beta \) can be adjusted accordingly to convert the Gibbs energy change to joules per mole. Equation ( 2 ) establishes a connection between Henry’s law constant and the product of the liquid’s surface tension and the van der Waals radius, along with the volume energy, all in relation to temperature.

For a semi-empirical model, a relationship between Henry’s law constants and the energy properties that characterize the noble gas transition between gas and dissolved gas states is established. This encompasses the capability of the model to analyze the contribution to the Gibbs energy of two components: the volumetric free energy and the surface free energy of both gas molecules and the solvent. The overall change in the Gibbs free energy ( \(\Delta G =\Delta G_{\gamma } + \Delta G_v\) , ) of a component system can include contributions from both surface and volume energies, as given by the following expression:

where \(R=\) 8.3145  [J/(mol K)] is the ideal gas constant, r is the van der Waals radius in angstrom units, and T is temperature in \(\text {K}\) . The surface tension (in erg/cm 2 ) of a liquid salt decreases linearly with the change in temperature while maintaining a constant pressure, given by the expression

The enthalpy change is determined to be independent of temperature, as evidenced by

The entropy change is obtained from the relationship between Gibbs free energy and enthalpy as follows:

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The solubility of noble gases by Henry’s gas constant were calculated as a function of temperature in a molten salt mixture, two eutectic mixtures of 2LiF– \({{\hbox {BeF}}_{2}}\) (Flibe) and and LiF–NaF–KF (Flinak). This semi-empirical method to calculate \(\alpha \) and \(\beta \) parameters assumes that the noble gas phase evaporative process is temperature-dependent. Henry’s law constants for helium, neon, argon, krypton, and xenon in 2LiF– \({{\hbox {BeF}}_{2}}\) (64–36 mol%) and LiF–NaF–KF (46.5–11.5–42.0 mol%) solutions at various temperatures were used to benchmark gas solubility in this study. These constants were utilized in the regression fit of the data. Figure  2 represents the change in Henry’s law constant with temperature.

The objective of this analysis was to ascertain \(\alpha \) , \(\beta \) , and \(K_H^0\) values by the regression in Table 1 , and each set of values was shown to remain constant for all five noble gases dissolved in 2LiF– \({{\hbox {BeF}}_{2}}\) and LiF–NaF–KF along with the corresponding surface tension. In Flibe, \(\beta \) is negative, while in Flinak, \(\beta \) is positive. Flinak is composed exclusively of alkali fluorides that behave as separate ions in the melt. In FLibe, the characteristic of a negative \(\beta \) arises from the behavior of beryllium fluoride in the melt. The chemistry of beryllium, being an alkaline earth, is different from that of the alkali metals. \({{\hbox {BeF}}_{2}}\) is nonionic and associates in solution, and this property is ultimately responsible for its high viscosity. The melting point of \({{\hbox {BeF}}_{2}}\) is 827 (in K), which is lower than NaF 1266 (in K) and KF 1131 (in K) 6 . As long as the salt temperature remains above the melting point of \({{\hbox {BeF}}_{2}}\) , this volume energy contribution is negative ( \(\Delta G_v<0\) ). However, when the salt temperature falls below the melting point of NaF and KF, this volume energy contribution becomes positive ( \(\Delta G_v>0\) ). Simultaneously, van der Waals radius values were incorporated; the model regression effectively fits the experimental data (with the exclusion of all helium temperature point in the Fig.  2 ). Discrepancies between the model and all helium data point are likely due to polarization effects at the subatomic level caused by the helium only having duet electrons in the full outer shell as opposed to the octet shells of the larger gases. This means that helium has a less dramatic polarization due to London dispersion forces 7 . Also, in helium, the experimental data did not align in 2LiF– \({{\hbox {BeF}}_{2}}\) 8 , 9 . However, a notable level of agreement was apparent from the fit of the Henry’s law data for neon, argon, and xenon in \(2\hbox {LiF}-{{\hbox {BeF}}_{2}}\) on the left side of Fig.  2 , as well as for neon and argon in LiF–NaF–KF on the right side of Fig.  2 . The model predictions were employed to generate a dataset to conduct a comparative analysis between the noble gases experimental measurements. The model was used to predict the Henry’s law constant for both helium and krypton ( \(2\hbox {LiF}-{{\hbox {BeF}}_{2}}\) ) and helium, krypton, and xenon (LiF–NaF–KF), as shown in Fig.  2 ; data were unavailable for the latter.

The change in Gibbs free energy in 2LiF– \({{\hbox {BeF}}_{2}}\) system has been amended to include the appropriate correction for Henry’s gas constant. This corrected equation is then utilized in a nonlinear regression approach that takes into account both the surface and volume energy terms of the Gibbs energy. Equation ( 2 ) considers temperature variations and the van der Waals radii of noble gases. The measured solubilities of neon, argon, and xenon gases play a crucial role as input data points for generating the regressed parameters. By employing nonlinear regression analysis with the entirety of this data, it was possible to predict helium and krypton values’ solubilities in 2LiF– \({{\hbox {BeF}}_{2}}\) . Additionally, the analysis allowed for the prediction of helium, krypton, and xenon in LiF–NaF–KF. These projections give clearly defined \(\alpha \) and \(\beta \) parameters that are inherent to 2LiF– \({{\hbox {BeF}}_{2}}\) and LiF–NaF–KF salts.

The change in Gibbs free energy within the 2LiF−  \({{\hbox {BeF}}_{2}}\) and LiF–NaF–KF system is closely tied to the van der Waals radius. The radius for each noble gas in the system involves an evaluation of the two key components of Gibbs free energy analysis: volume energy and surface energy. Volume energy gives the potential for a phase transition—either evaporation or condensation—to occur. Whereas surface energy quantifies the energy necessary for interface formation. The surface and volume energies are clearly shown along with the cumulative sum.

The volume and surface energy functions change directly in relation to the cube of the van der Waals radius and the square of the van der Waals radius, respectively. Both volume energy and surface energy are shown separately, and their combined total is also illustrated in 2LiF– \({{\hbox {BeF}}_{2}}\) and LiF–NaF-KF.

The graph reveals the temperature dependency of \(\Delta G\) in the vaporization of noble gases. \(\Delta G\) varies with temperature, whereas \(\Delta H\) remains constant. As expressed by \(\Delta G = \Delta H - T \Delta S\) , at this specific temperature, \(\Delta G \) is less than 0, \(\Delta H\) is greater than 0, and \( T \Delta S\) is greater than 0. As a result, noble gases undergo spontaneous evaporation from 2LiF– \({{\hbox {BeF}}_{2}}\) and and LiF–NaF–KF. The enthalpy of solution indicates the quantity of heat absorbed. This reaction is consistently endothermic ( \(\Delta H > 0\) ) due to the necessity of sufficient energy to escape the interactions at a constant pressure throughout the dissolution process. The increase in temperature effectively can be seen as adding the energy required to increase the gas to liquid contact surface area.

Figure  3 shows how the change in Gibbs free energy, as determined by the interplay of surface energy and volume energy from Eq. ( 2 ), depends on the value of the van der Waals radius on the x-axis. The individual contributions of surface energy and volume energy can be observed, and the cumulative amount is displayed. The surface energy has a greater influence than the volume energy. In all cases, the Gibbs energy change ( \(\Delta G\) ) for each noble gas exhibited a decrease with increased radius. Consequently, thermodynamic equilibrium within the molten state leads to a feedback release of energy, facilitating rapid vapor formation and driving the system toward the lowest possible Gibbs energy state. Much like the interactions of surface and volume energies, Fig.  4 illustrates the change of \(\Delta G\) with temperature. As the temperature increases, in Eq. ( 2 ), the surface energy increases and the volume energy decreases, but the total contribution increases.

The spontaneity of a reaction depends on changes in both enthalpy and entropy. This is highlighted by the invariant nature of \(\Delta H\) coupled with decreasing \(\Delta S\) with increasing temperature. This pattern corresponds to increasing values of Henry’s gas constant in 2LiF– \({{\hbox {BeF}}_{2}}\) and LiF–NaF–KF.

From the Gibbs equation, it can be seen if the change in Gibbs energy is negative and the change in enthalpy and entropy will be positive, the transition is an endothermic process. Figure  5 shows the change in Gibbs free energy and enthalpy as a function of temperature for noble gases. In most reactions, enthalpy is associated with the heat capacity as outlined in Eq. ( 4 ), and it remains relatively stable across varying temperatures. Entropy from Eq. ( 5 ) is the difference between Gibbs energy and enthalpy change, as shown in Fig.  6 . The literature showed enthalpy change and entropy change from the \(K_H^e\) with temperature 8 . Conventionally, the natural logarithm of \(K_H^e\) is plotted against the inverse of temperature (1/ T ) and therefore a linear regression can be used to determine changes in enthalpy and entropy. The resulting straight line has a slope of \(-\Delta H/R\) and an intercept of \(\Delta S/R\) , as shown in Table 2 . Table 2 presents a comparison of values. The enthalpy value is compared to both the reference method or experimental data and our model. The relative percent difference (RPD), the absolute difference value divided by the mean, is within 5.5%. Based on the van der Waals radius, the noble gases’ elements exhibit distinct effects on the parameters \(\alpha \) , \(\beta \) and \(K_H^0\) . These parameters are intricately tied to the interaction of the dissolved gas molecules’ radius with the ionic environment within the melt. An exponential relationship exists between Henry’s law constant and the Gibbs energy \(\Delta G\) . Although \(\Delta G\) is associated with surface energy 8 , 11 , this model was introduced to incorporate Gibbs volumetric energy. The enthalpy term of the \(\ln {K_H^e}\) method and our model remains constant at a given temperature. The entropy of the model varies with temperature while the \(\ln {K_H^e}\) method remains constant, making comparison difficult.

Conclusions

This paper establishes connections among several physicochemical parameters by effectively linking them to contributions to the Gibbs energy of gas transport through a two-layer film interface. Surface and volume terms for Gibbs free energies were used to show enthalpic and entropic trends. The findings demonstrate significant alignment with pertinent experimental data. As a result, forecasts for Henry’s gas constant values pertaining to helium, krypton, or xenon were formulated, establishing a crucial foundation for future experimental applications and theoretical inquiries. The Gibbs free energy associated with liquid–gas interfaces and volumes is determined by the van der Waals radius of each noble gas. In this work, we introduce a refined and comprehensive extension of this theory. Notably, our findings reveal that as temperature rises, noble gases situated in the interfacial region between liquid and gas phases exhibit a noteworthy volumetric energy contribution.

Data availability

All data generated or analyzed during this study are included in this published article and its Supplementary Files.

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Acknowledgements

This work was performed in the framework of the NEAMS program supported by the U.S. Department of Energy.

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Kyoung O. Lee, Wesley C. Williams, Joanna McFarlane, David Kropaczek & Dane de Wet

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Lee, K.O., Williams, W.C., McFarlane, J. et al. Semi-empirical model for Henry’s law constant of noble gases in molten salts. Sci Rep 14 , 12847 (2024). https://doi.org/10.1038/s41598-024-60006-9

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DOI : https://doi.org/10.1038/s41598-024-60006-9

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Bhopal Gas Tragedy : Causes, effects and aftermath

The Bhopal gas tragedy occurred at midnight of December 2nd- 3rd December 1984 at the Union Carbide India Ltd (UCIL) pesticide facility in Bhopal, Madhya Pradesh. This catastrophe affected around 500,000 people along with many animals. People who were exposed are still suffering as a result of the gas leak’s long-term health impacts. Chronic eye difficulties and respiratory problems were some issues due to it. Children who have been exposed have stunted growth and cognitive impairments. 

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Bhopal Gas Tragedy

Bhopal gas tragedy case study, causes of bhopal gas tragedy, effects of bhopal gas tragedy, aftermath of bhopal gas tragedy.

Union Carbide was an American company that produced pesticides. MIC – methyl isocyanide, a dangerous poisonous gas began to leak at midnight on 2nd December 1984 from the Union Carbide factory. This MIC caused the Bhopal gas tragedy. The Bhopal gas tragedy was a fatal accident. It was one of the world’s worst industrial accidents. 

UCIL was a pesticide manufacturing plant that produced the insecticide carbaryl. Carbaryl was discovered by the American company Union Carbide Corporation, which owned a significant share in UCIL. As an intermediary, UCIL produced carbaryl using methyl isocyanate (MIC). Other techniques for producing the ultimate product are available, but they are more expensive. The very toxic chemical MIC is extremely dangerous to human health. Residents of Bhopal in the area of the pesticide plant began to feel irritated by the MIC and began fleeing the city.

Bhopal UCIL constructed three underground MIC storage tanks which were named E610, E611, and E619. On October 1984, E610 was not able to maintain its nitrogen gas pressure and so the liquid which is present inside the tank would not pump out, because of which 42 tons of MIC in E610 was wasted. The chemical in E610 was left unpumped as they were not able to re-establish its pressure, which later became responsible for Bhopal Gas Tragedy.

The main causes of Bhopal Gas Tragedy are as follows:

• During the buildup to the spill, the plant’s safety mechanisms for the highly toxic MIC were not working. The alarm off tanks of the plant had not worked properly.
• Many valves and lines were in disrepair, and many vent gas scrubbers were not working, as was the steam boiler that was supposed to clean the pipes.
• The MIC was stored in three tanks, with tank E610 being the source of the leak. This tank should have held no more than 30 tonnes of MIC, according to safety regulations.
• Water is believed to have entered the tank through a side pipe as technicians were attempting to clear it late that fatal night.
• This resulted in an exothermic reaction in the tank, progressively raising the pressure until the gas was ejected through the atmosphere.

The main effects of the Bhopal Gas Tragedy are as follows:

• Thousands had died as a result of choking, pulmonary edema, and reflexogenic circulatory collapse.
• Neonatal death rates increased by 200 percent.
• A huge number of animal carcasses have been discovered in the area, indicating the impact on flora and animals. The trees died after a few days. Food supplies have grown scarce due to the fear of contamination. 
• Fishing was also prohibited.
• In March 1985, the Indian government established the Bhopal Gas Leak Accident Act, giving it legal authority to represent all victims of the accident, whether they were in India or abroad.
• At least 200,000 youngsters were exposed to the gas.
• Hospitals were overcrowded, and there was no sufficient training for medical workers to deal with MIC exposure.

In the United States, UCC was sued in federal court. In one action, the court recommended that UCC pay between $5 million and $10 million to assist the victims. UCC agreed to pay a $5 million settlement. The Indian government, however, rejected this offer and claimed $3.3 billion. In 1989, UCC agreed to pay $470 million in damages and paid the cash immediately in an out-of-court settlement.

Warren Anderson, the CEO and Chairman of UCC was charged with manslaughter by Bhopal authorities in 1991. He refused to appear in court and the Bhopal court declared him a fugitive from justice in February 1992. Despite the central government’s efforts in the United States to extradite Anderson, nothing happened. Anderson died in 2014 without ever appearing in a court of law.

Bhopal Gas Tragedy continues to be an important warning sign for industrialization, for developing countries and in particular India, with human, environmental, and economic pitfalls. The economy of India is growing at a fast rate but at the cost of environmental health as well as public safety.

Frequently Asked Questions

What were the reasons behind bhopal gas tragedy.

The reasons behind Bhopal gas tragedy was a large volume of water had been introduced into the MIC tank and has caused a chemical reaction which did force the pressure release valve, which allowed the gas to leak.

What is the name of Bhopal gas case law?

The name is Union Carbide Corporation v.

Which gas was leaked in the Bhopal Gas Tragedy?

The gas which was leaked in the Bhopal Gas Tragedy is methyl isocyanate.

Was Bhopal gas tragedy an accident or experiment?

Bhopal gas tragedy was the world’s most worst industrial accident.

How many people died in the Bhopal Gas?

A total of 3,787 deaths were registered related to the gas release in case of Bhopal Gas Tragedy.

What were the four main demands of the Bhopal Gas victims?

The 4 demands of Bhopal Gas victims include: Proper medical treatment. Adequate compensation. Fixation of criminal responsibility Steps for prevention of such disasters in future.

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Bhopal Gas Tragedy was fixed with construction of a secure landfill for holding the wastes from the two on-site solar evaporation ponds.

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What is the second law of thermodynamics?

The second law of thermodynamics says, in simple terms, entropy always increases. This principle explains, for example, why you can't unscramble an egg.

Work and energy

The arrow of time.

• Fate of the universe

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The second law of thermodynamics states that as energy is transferred or transformed, more and more of it is wasted. It's one of the four laws of thermodynamics , which describe the relationships between thermal energy, or heat, and other forms of energy, and how energy affects matter. The First Law of Thermodynamics states that energy cannot be created or destroyed; the total quantity of energy in the universe stays the same. The Second Law of Thermodynamics is about the nature of energy. The Second Law also states that there is a natural tendency of any isolated system to degenerate into a more disordered state, according to Boston University .

Saibal Mitra, a professor of physics at Missouri State University, finds the Second Law to be the most interesting of the four laws of thermodynamics. "There are a number of ways to state the Second Law," Mitra told Live Science. "At a very microscopic level, it simply says that if you have a system that is isolated, any natural process in that system progresses in the direction of increasing disorder, or entropy, of the system." 

Mitra explained that all processes result in an increase in entropy. Even when order is increased in a specific location, for example by the self-assembly of molecules to form a living organism, when you take the entire system including the environment into account, there is always a net increase in entropy. In another example, crystals can form from a salt solution as the water is evaporated. Crystals are more orderly than salt molecules in solution; however, vaporized water is much more disorderly than liquid water. The process taken as a whole results in a net increase in disorder.

History of the second law of thermodynamics

In his book, " A New Kind of Science " (Wolfram Media, 2018), Stephen Wolfram wrote, "Around 1850 Rudolf Clausius and William Thomson (Lord Kelvin) stated that heat does not spontaneously flow from a colder body to a hotter body." This became the basis for the Second Law. 

Subsequent works by Daniel Bernoulli , James Clerk Maxwell , and Ludwig Boltzmann led to the development of the kinetic theory of gases, in which a gas is recognized as a cloud of molecules in motion that can be treated statistically, according to Georgia State University . This statistical approach allows for precise calculation of temperature , pressure and volume according to the ideal gas law, according to Georgia State University. 

This approach also led to the conclusion that while collisions between individual molecules are completely reversible, i.e., they work the same when played forward or backward, that's not the case for a large quantity of gas. With large quantities of gas, the speeds of individual molecules tend over time to form a normal or Gaussian distribution, sometimes depicted as a "bell curve," around the average speed. The result of this is that when hot gas and cold gas are placed together in a container, you eventually end up with warm gas, according to Georgia State University . However, the warm gas will never spontaneously separate itself into hot and cold gas, meaning that the process of mixing hot and cold gases is irreversible. This has often been summarized as, "You can't unscramble an egg." According to Wolfram, Boltzmann realized around 1876 that the reason for this is that there must be many more disordered states for a system than there are ordered states; therefore random interactions will inevitably lead to greater disorder.

One thing the Second Law dictates is that it is impossible to convert heat energy to mechanical energy with 100% efficiency, according to Britannica . After the process of heating a gas to increase its pressure to drive a piston, there is always some leftover heat in the gas that cannot be used to do any additional work. This waste heat must be discarded by transferring it to a heat sink. In the case of a car, this is done by sending the spent fuel and air mixture from the engine to the atmosphere via the exhaust pipe. Additionally, any device with movable parts produces friction that converts mechanical energy to heat that is generally unusable and must be removed from the system by transferring it to a heat sink. This is why claims for perpetual motion machines are summarily rejected by the U.S. Patent Office. 

When a hot and a cold body are brought into contact with each other, heat energy will flow from the hot body to the cold body until they reach thermal equilibrium , i.e., the same temperature. However, the heat will never move back the other way; the difference in the temperatures of the two bodies will never spontaneously increase. Moving heat from a cold body to a hot body requires work to be done by an external energy source such as a heat pump, according to Georgia State University . 

"The most efficient engines we build right now are large gas turbines," said David McKee, a professor of physics at Missouri State University. "They burn natural gas or other gaseous fuels at a very high temperature, over 2,000 degrees Celsius [3,600 degrees Fahrenheit], and the exhaust coming out is just a stiff, warm breeze. Nobody tries to extract energy from the waste heat, because there's just not that much there."

The Second Law indicates that thermodynamic processes, i.e., processes that involve the transfer or conversion of heat energy, are irreversible because they all result in an increase in entropy. Perhaps one of the most consequential implications of the Second Law, Mitra said, is that it gives us the thermodynamic arrow of time.

In theory, some interactions, such as collisions of rigid bodies or certain chemical reactions, look the same whether they are run forward or backward. In practice, however, all exchanges of energy are subject to inefficiencies, such as friction and radiative heat loss, which increase the entropy of the system being observed, according to OpenStax . Therefore, because there is no such thing as a perfectly reversible process, if someone asks what is the direction of time, we can answer with confidence that time always flows in the direction of increasing entropy.

The fate of the universe

—  What is thermodynamics?

—  What is the zeroth law of thermodynamics?

—  What is the first law of thermodynamics?

—  What is the third law of thermodynamics?

The Second Law also predicts the end of the universe, according to Boston University. "It implies that the universe will end in a 'heat death' in which everything is at the same temperature. This is the ultimate level of disorder; if everything is at the same temperature, no work can be done, and all the energy will end up as the random motion of atoms and molecules."

In the far distant future, stars will cease being born, galaxies will burn out, and black holes will evaporate until there's nothing left but subatomic particles and energy, according to Science Magazine . Ultimately, those particles and that energy will reach thermal equilibrium with the rest of the Universe. Fortunately, John Baez, a mathematical physicist at the University of California Riverside, predicts that this process of cooling down could take as long as 10 (10^26)  (1 followed by 10 26 (100 septillion) zeros) years with the temperature dropping to around 10 −30  K (10 −30  C above  absolute zero ).

Live Science contributor Ashley Hamer updated this article on Jan. 27, 2022.

Here are some other explanations of the second law of thermodynamics:

• This video from the World Science Festival explores entropy and the arrow of time with physicist Brian Greene.
• Get another explanation of the second law of thermodynamics in this resource from the University of Calgary .
• George Mason University earth science professor Robert M. Hazen discusses the consequences of the second law of thermodynamics in this article from The Great Courses Daily .

Boston University, "Entropy and the second law," December 12, 1999. http://physics.bu.edu/~duffy/py105/Secondlaw.html  

Stephen Wolfram, "A New Kind of Science," Wolfram Media, 2018. http://www.wolframscience.com/nksonline/toc.html  

Famous Scientists, "Daniel Bernoulli." https://www.famousscientists.org/daniel-bernoulli/  

Famous Scientists, "James Clerk Maxwell." https://www.famousscientists.org/james-clerk-maxwell/  

Famous Scientists, "Ludwig Boltzmann." ​​ https://www.famousscientists.org/ludwig-boltzmann/  

Georgia State University Hyperphysics, "Kinetic Theory." http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kinthe.html  

Georgia State University Hyperphysics, "Ideal Gas Law." http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/idegas.html#c1  

Georgia State University Hyperphysics, "Gaussian Distribution Function." http://hyperphysics.phy-astr.gsu.edu/hbase/Math/gaufcn.html  

Britannica, "Entropy." June 1, 2021. https://www.britannica.com/science/thermodynamics/Entropy  

Georgia State University Hyperphysics, "Heat Pump." http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatpump.html  

Openstax University Physics 2, "21 Reversible and Irreversible Processes." July 16, 2019. https://opentextbc.ca/universityphysicsv2openstax/  

Adam Mann, "This is the way the universe ends: not with a whimper, but a bang," August 11 2020, Science Magazine. https://www.science.org/content/article/way-universe-ends-not-whimper-bang  

John Baez, "The End of the Universe." February 7, 2016. https://math.ucr.edu/home/baez/end.html  

Cool Cosmos, "What is absolute zero?" https://coolcosmos.ipac.caltech.edu/ask/298-What-is-absolute-zero-  

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Together Against Trafficking in Human Beings

Trafficking in human beings is a crime that should have no place in today’s society. It destroys individuals’ lives by depriving people of their dignity, freedom and fundamental rights. It is often a violent crime committed by organised crime networks.

Facts about trafficking in human beings

37% of the victims of trafficking in the EU are EU citizens, and a significant number of them are trafficked within their own country. However, non-EU victims have increased in recent years and they now outnumber victims with an EU citizenship. The majority of victims in the EU are women and girls who are mainly trafficked for sexual exploitation. The ratio of male victims has more than doubled in the last years.

Around 15% of victims of trafficking in the EU are children.

The most common forms of trafficking in the EU is sexual exploitation and labour exploitation . Both forms of exploitation amount to an equal share of victims. Most traffickers in the EU are EU citizens and often of the same nationality as their victims. More than three quarters of perpetrators are men.

Links with organised crime

This crime brings high profits to criminals and carries with it enormous human, social and economic costs. Trafficking in human beings is often linked with other forms of organised crime such as migrant smuggling, drug trafficking, extortion, money laundering, document fraud, payment card fraud, property crimes, cybercrime and other.

This complex criminal phenomenon continues to be systematically addressed in a wide range of EU policy areas and initiatives from security to migration, justice, equality, fundamental rights, research, development and cooperation, external action and employment to name a few.

Discover the 'End human trafficking. Break the invisible chain' campaign

Learn about EU Anti-trafficking actions

A comprehensive EU approach to fight trafficking in human beings is anchored in the EU Anti-trafficking Directive, and complemented by the EU Strategy on Combatting Trafficking in Human Beings (2021-2025).

The EU Anti-Trafficking Coordinator is responsible for improving coordination and coherence among EU institutions, EU agencies, Member States and international actors, and for developing existing and new EU policies to address Trafficking in Human Beings.

Part of the mandate of the EU Anti-Trafficking Coordinator is to foster cooperation and policy coherence, including the EU Networks of the National Rapporteurs and Equivalent Mechanisms, the EU Civil Society Platform and the cooperation with the EU Agencies.

This section provides comprehensive information on how each EU country, tackles, prevents and identifies instances of trafficking in human beings.

Recent calls for proposals and EU projects and Funding for projects addressing trafficking in human beings are presented.

This section provides an overview of relevant publications and studies on EU anti-trafficking actions.

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Civil rights groups, state of Iowa make case for, against new 'illegal reentry' law

Civil rights groups made their case in federal court Monday against the state's new immigration law , which criminalizes "illegal reentry" and allows local authorities to arrest and deport undocumented immigrants who return to the United States.

U.S. District Judge Stephen Locher heard arguments in a packed courtroom for two separate lawsuits, each requesting an injunction on Senate File 2340 before it takes effect July 1. The Department of Justice filed its lawsuit against the state in early May , the same day as the groups — the American Immigration Council, American Civil Liberties Union and ACLU of Iowa — filed theirs on behalf of Iowa Migrant Movement for Justice.

Senate File 2340 states that any person previously deported or denied entry to the U.S. would be barred from entering Iowa. The crime would be an aggravated misdemeanor in most cases but could become a felony under certain circumstances, including if the person was arrested for allegedly committing another felony.

Christopher Eiswerth, an attorney for the DOJ, and Emma Winger, the council's deputy legal director, told Locher the new law is unconstitutional, conflicts with existing federal immigration policies and could impact the nation's future relationships with foreign countries. They said the law — which carries a prison sentence of up to 10 years — could also impact people seeking asylum and other temporary protected statuses or legal citizens who were previously deported.

"Just because they were removed one time, it doesn't mean that they're forever banned from the states," Eiswerth said.

More: Iowa's new immigration law relies on local police, but many doubt they can enforce it

That's on top of a 2012 Supreme Court decision that ruled that states cannot implement their own immigration laws.

Iowa's law has  spurred harsh opposition from immigration advocates , as well as  questions from police and county attorneys  who so far have received no guidance on how to enforce the law or prosecute cases involving it. SF 2340 mirrors a Texas law that has been blocked by the courts while a lawsuit challenging its constitutionality is decided.

"You might not know the minutiae of it, but we know how it's going to work," Winger said. A state judge can order a person convicted under the law be deported back to their country of origin — "not the port of entry," she said.

'Let the law play out,' state says

But Patrick Valencia, deputy solicitor general for the Iowa attorney general's office, argued SF 2340 "sets standards," allowing the state to "enforce those federal rights." He said Iowa is "presumed" to follow the constitution.

Locher, who pointed out the new law introduces a pair of new crimes, asked Valencia why the Iowa law "left out" some language detailing exceptions especially since it was modeled after a Texas immigration law. That language could have been left out "for a reason," Locher said.

"Let the law play out," Valencia said. "We can't assume the law will be interpreted unconstitutionally."

Gov. Kim Reynolds and Attorney General Brenna Bird, both Republicans, have signaled they intend to defend the law, which passed the GOP-led Iowa Legislature and was  signed into law in April . 

In a statement Monday, Bird said President Joe Biden is not enforcing immigration laws in the country, so "Iowa is doing the job for him."

"Biden’s open borders have not only caused record illegal immigration, but they have opened the door for drug cartels, human traffickers, and suspected terrorists to enter our country," she said. "Today, we made the case in court defending Iowa’s law that prohibits illegal reentry and keeps our communities safe. If Biden invested half as much energy into securing our borders as he does suing states like Iowa, we would all be better off.”

Locher said he will rule on the injunction prior to July 1.

During a news conference held outside, Winger said this law would be "unique" if it were enforced and the judge's decision could set a precedent for other states that may be considering their own laws.

"If these laws aren't challenged, we're risking a situation where we have 50 states with 50 immigration polices — an unworkable system that will harm our vibrant immigrant communities across the country," Winger said.

More: 'Divisive and harmful': Iowa immigrants fear racial profiling with new 'illegal reentry' law

Erica Johnson, executive director of Iowa Migrant Movement for Justice, told reporters the U.S. needs an immigration system that is "workable" and humane."

"The problem is that Senate File 2340 is just the opposite of that. It's unworkable," Johnson said. "It's creating fear and driving misinformation in immigrant communities around our state. Supporters of the law say that they passed it because they were tired of the way the federal government was handling immigration.

"But again, this law is no solution to that."

Before and during the hearing, faith leaders, Latino families and members of IMMJ, Escucha Mi Voz and Iowa City Catholic Worker gathered outside the federal courthouse. One sign held up high above the more than 100 protesters read: "No tengo miedo a marchar y defienda la dignidad humana": "I am not afraid to march and defend human dignity." 

F. Amanda Tugade covers social justice issues for the Des Moines Register. Email her at  [email protected]  or follow her on Twitter  @writefelissa .

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Marketing to People with Disabilities: Case Studies and Campaigns

By Joanna Fragopoulos     June 14, 2024    

Marketing to people with disabilities starts with creating content and campaigns that resonate with them using real-life stories and situations. Below are case studies and campaigns that are inclusive to people with disabilities.

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5.3: The Gas Laws and Their Experimental Foundations

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Learning Objectives

• To understand the relationships among pressure, temperature, volume, and the amount of a gas.

Early scientists explored the relationships among the pressure of a gas ( P ) and its temperature ( T ), volume ( V ), and amount ( n ) by holding two of the four variables constant (amount and temperature, for example), varying a third (such as pressure), and measuring the effect of the change on the fourth (in this case, volume). The history of their discoveries provides several excellent examples of the scientific method .

The Relationship between Pressure and Volume: Boyle's Law

As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together. Conversely, as the pressure on a gas decreases, the gas volume increases because the gas particles can now move farther apart. Weather balloons get larger as they rise through the atmosphere to regions of lower pressure because the volume of the gas has increased; that is, the atmospheric gas exerts less pressure on the surface of the balloon, so the interior gas expands until the internal and external pressures are equal.

The Irish chemist Robert Boyle (1627–1691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury, as shown in Figure \(\PageIndex{1}\). In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample. The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Data such as those from one of Boyle’s own experiments may be plotted in several ways (Figure \(\PageIndex{2}\)). A simple plot of \(V\) versus \(P\) gives a curve called a hyperbola and reveals an inverse relationship between pressure and volume: as the pressure is doubled, the volume decreases by a factor of two. This relationship between the two quantities is described as follows:

\[PV = \rm constant \label{10.3.1} \]

Dividing both sides by \(P\) gives an equation illustrating the inverse relationship between \(P\) and \(V\):

\[V=\dfrac{\rm const.}{P} = {\rm const.}\left(\dfrac{1}{P}\right) \label{10.3.2} \]

\[V \propto \dfrac{1}{P} \label{10.3.3} \]

where the ∝ symbol is read “is proportional to.” A plot of V versus 1/ P is thus a straight line whose slope is equal to the constant in Equations \(\ref{10.3.1}\) and \(\ref{10.3.3}\). Dividing both sides of Equation \(\ref{10.3.1}\) by V instead of P gives a similar relationship between P and 1/ V . The numerical value of the constant depends on the amount of gas used in the experiment and on the temperature at which the experiments are carried out. This relationship between pressure and volume is known as Boyle’s law, after its discoverer, and can be stated as follows: At constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure. This law in practice is shown in Figure \(\PageIndex{2}\).

At constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure

The Relationship between Temperature and Volume: Charles's Law

Hot air rises, which is why hot-air balloons ascend through the atmosphere and why warm air collects near the ceiling and cooler air collects at ground level. Because of this behavior, heating registers are placed on or near the floor, and vents for air-conditioning are placed on or near the ceiling. The fundamental reason for this behavior is that gases expand when they are heated. Because the same amount of substance now occupies a greater volume, hot air is less dense than cold air. The substance with the lower density—in this case hot air—rises through the substance with the higher density, the cooler air.

The first experiments to quantify the relationship between the temperature and the volume of a gas were carried out in 1783 by an avid balloonist, the French chemist Jacques Alexandre César Charles (1746–1823). Charles’s initial experiments showed that a plot of the volume of a given sample of gas versus temperature (in degrees Celsius) at constant pressure is a straight line. Similar but more precise studies were carried out by another balloon enthusiast, the Frenchman Joseph-Louis Gay-Lussac (1778–1850), who showed that a plot of V versus T was a straight line that could be extrapolated to a point at zero volume, a theoretical condition now known to correspond to −273.15°C (Figure \(\PageIndex{3}\)).A sample of gas cannot really have a volume of zero because any sample of matter must have some volume. Furthermore, at 1 atm pressure all gases liquefy at temperatures well above −273.15°C. Note from part (a) in Figure \(\PageIndex{3}\) that the slope of the plot of V versus T varies for the same gas at different pressures but that the intercept remains constant at −273.15°C. Similarly, as shown in part (b) in Figure \(\PageIndex{3}\), plots of V versus T for different amounts of varied gases are straight lines with different slopes but the same intercept on the T axis.

The significance of the invariant T intercept in plots of V versus T was recognized in 1848 by the British physicist William Thomson (1824–1907), later named Lord Kelvin. He postulated that −273.15°C was the lowest possible temperature that could theoretically be achieved, for which he coined the term absolute zero (0 K).

We can state Charles’s and Gay-Lussac’s findings in simple terms: At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in kelvins). This relationship, illustrated in part (b) in Figure \(\PageIndex{3}\) is often referred to as Charles’s law and is stated mathematically as

\[V ={\rm const.}\; T \label{10.3.4} \]

\[V \propto T \label{10.3.5} \]

with temperature expressed in kelvins, not in degrees Celsius. Charles’s law is valid for virtually all gases at temperatures well above their boiling points.

The Relationship between Amount and Volume: Avogadro's Law

We can demonstrate the relationship between the volume and the amount of a gas by filling a balloon; as we add more gas, the balloon gets larger. The specific quantitative relationship was discovered by the Italian chemist Amedeo Avogadro, who recognized the importance of Gay-Lussac’s work on combining volumes of gases. In 1811, Avogadro postulated that, at the same temperature and pressure, equal volumes of gases contain the same number of gaseous particles (Figure \(\PageIndex{4}\)). This is the historic “Avogadro’s hypothesis.”

A logical corollary to Avogadro's hypothesis (sometimes called Avogadro’s law) describes the relationship between the volume and the amount of a gas: At constant temperature and pressure, the volume of a sample of gas is directly proportional to the number of moles of gas in the sample. Stated mathematically,

\[V ={\rm const.} \; (n) \label{10.3.6} \]

\[V \propto.n \text{@ constant T and P} \label{10.3.7} \]

This relationship is valid for most gases at relatively low pressures, but deviations from strict linearity are observed at elevated pressures.

For a sample of gas,

• V increases as P decreases (and vice versa)
• V increases as T increases (and vice versa)
• V increases as n increases (and vice versa)

The relationships among the volume of a gas and its pressure, temperature, and amount are summarized in Figure \(\PageIndex{5}\). Volume increases with increasing temperature or amount, but decreases with increasing pressure.

The volume of a gas is inversely proportional to its pressure and directly proportional to its temperature and the amount of gas. Boyle showed that the volume of a sample of a gas is inversely proportional to its pressure ( Boyle’s law ), Charles and Gay-Lussac demonstrated that the volume of a gas is directly proportional to its temperature (in kelvins) at constant pressure ( Charles’s law ), and Avogadro postulated that the volume of a gas is directly proportional to the number of moles of gas present ( Avogadro’s law ). Plots of the volume of gases versus temperature extrapolate to zero volume at −273.15°C, which is absolute zero (0 K) , the lowest temperature possible. Charles’s law implies that the volume of a gas is directly proportional to its absolute temperature.

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A new movie tells the story of Kemba Smith Pradia, race and incarceration

Strange news, meet abby lampe, two-time champion of the cheese-wheel-chasing race, meet abby lampe, two-time champion of the chees-wheel-chasing race, 100 years ago, indigenous people were granted u.s. citizenship by law.

by  Sandhya Dirks

The first professional women's hockey league in the U.S. has a winner

Music interviews, jon lampley, a veteran of stephen colbert's talk show, releases his debut album.

by  D. Parvaz ,  Ayesha Rascoe ,  Ryan Benk

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