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Introduction

This law was named after the French Chemist Gay Lussac, who discovered the relationship between the pressure of a gas and its absolute temperature. Gay Lussac’s law of Thermodynamics state that when the volume is held constant, the pressure of the given mass of gas varies directly with the gas’s absolute temperature. The kinetic energy of the molecules of the gas increases, which in turn hits the walls of the container with greater force, resulting in greater pressure. Mathematically, it can be written as P/T=k. It is a special case of ideal law gas. This law is also commonly known as the Pressure Law or Amontons’s Law.

Mathematical Expression of the Law

P∝T  (Volume constant)

Removing the proportionality-

P=kT     —(1)  

(here P= Pressure exerted by the gas

         k= constant

         T= absolute temperature of the gas)

For Ideal Gas Equation- 

PV=nRT       —(2)

Substituting the value of P from equation (1) to (2)-

kTV=nRT

k=nR/V

k∝1/V     —(3)

From the above equation, we see that when volume will increase and k(constant) will decrease.

The law can be written as follows for comparing the same substance under two different sets of conditions:

P1 T2  =  P2 T1

Graphical Representation of Gay Lussac’s Law

The graphical representation of this law is also known as the P-T graph. The graph is drawn by taking the absolute temperature on the x-axis and pressure on the y-axis. This relation is called the pressure-time relation. The slope in this graph represents k(constant) and is inversely proportional to the volume. Therefore, if we increase the volume, the slope will decrease. Here, it is given that V1 < V2 < V3 < V4 and the graph can be represented as follows:

The graph illustrates that the pressure of gas kept at a constant volume constantly decreases as it cools until the gas eventually condenses and becomes a liquid.

Law of Combining Volumes

The law of combining volumes states that when gasses react with each other, they react in volume, which takes up a simple whole-number ratio, provided that the temperature and pressure of the reacting gases remain constant. 

Statement- The ratio between the volumes of the reactant gasses and the gaseous products can be expressed in simple whole numbers.

For example, Gay Lussac discovered that two molecules of hydrogen combine with one molecule of oxygen to form two molecules of water. Based on these results, Amedeo Avogadro assumed that the same amount of gas contains the same number of molecules at the same temperature and pressure. This hypothesis can be expressed as:

2 molecules of hydrogen + 1 molecule of oxygen = 2 molecules of water.

Therefore, the volumes in which hydrogen and oxygen combine bear a simple ratio of 2:1.

About the Scientist- Gay Lussac

Joseph-Louis Gay Lussac is a French chemist and physicist. He initiated the study into the behavior of gasses and developed new techniques in the analysis and experimentation of the same, which led to notable advances in the field of applied chemistry. He was born on December 6, 1778 in France. Gay Lussac’s first publication came out in 1802, which dealt with the thermal expansion of gases. He used dry gasses and mercury for error-free results in the experiment. From the experiment that he performed, he concluded that all gasses expand equally in the temperature range of  0-100 ° C. This law is usually attributed to the “Charles Law.” These were the first of several regularities in the behaviour of matter that Gay Lussac established. Gay Lussac’s with his friend Louis Jacques Thenard, identified a class of substances (later called carbohydrates) such as sugar and starch that contained a 2: 1 ratio of hydrogen and oxygen. They published the results in the form of three laws, depending on the ratio of hydrogen to oxygen in the substance. 

Real-life Examples of Gay Lussac’s Law

  • Vehicle Tyre- Vehicles inflated tyres may burst on sweltering summer days. This bursting of tyres is due to Gay Lussac’s Law. There is a lot of pressure inside the inflated tyres, so when the temperature of the air inside the tyre rises, so does the pressure of the gas in the tube. The tyres fracture after reaching an unbearable point. 
  • Pressure Cooker- The pressure cooker is a sealed utensil that uses steam pressure to cook food. It is typically made of steel or aluminum. When heat is applied to the cooker, the water inside vaporizes, and steam is produced. To maintain the operating pressure inside the cooker, steam is periodically released through a valve. If the valve fails and the heat flow continues, the pressure inside the cooker rises. The pressure rise as stated on the Gay Lussac’s Law. This high pressure may cause the cooker to rupture, resulting in an unfortunate accident.
  • Water Heater- Electric water heaters are similar to pressure cookers. The heating filaments inside heat the cold water. The hot water produced is discharged through the outlet nozzle. Water temperature is automatically controlled by modern electric heaters. When the system and pressure-relief valve fail, a continuous power supply is used to generate steam. This steam has the potential to damage the heater. The heater may burst if the pressure of the steam exceeds the tolerable limit.
  • Aerosol Cans- Aerosol cans and sprays are devices that spray an aerosol, which is a suspension of fine solid particles or liquid droplets in the air. Gay Lussac’s Law is illustrated by the bursting of an aerosol can. When an aerosol can is exposed to high temperatures, the propellant vaporizes. These vaporized gasses exert pressure on the can’s wall. According to Gay Lussac’s Law, the pressure on the wall increases with temperature. Finally, when the pressure becomes unbearable, the can bursts. This is why it is recommended that aerosol cans be kept away from heat.

Conclusion


We learned about Gay Lussac’s Law of Thermodynamics. It is an important study to learn about the behavior of ideal gasses. Gay Lussac law has application in real life too. The significance of this gas law is that it shows that increasing the temperature of a gas causes a relative increase in its pressure (assuming that the volume does not change). Similarly, decreasing the temperature causes the pressure to decrease proportionally.