Mathematical Explanation of Boyle`s Law
The mathematical expression of Boyles` law is a constant pressure and volume, which can be expressed as P V = k, where P is the pressure, V is the volume and k is a constant. This means that for constant pressure, a constant volume must be maintained. This law can be seen in the illustration of an air column, where the pressure at the base increases as the column expands, while the pressure at the tip remains constant. This shows that as the volume of a substance increases, the pressure inside the substance also increases. According to Boyles` law, any change in the volume occupied by a gas (at constant quantity and temperature) causes a change in the pressure exerted by it. In other words, the product of the initial pressure and volume of a gas is equal to the product of the final pressure and final volume (at constant temperature and number of moles). This law can be expressed mathematically as follows: For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed mathematically as follows. In this article, we will talk about gas laws and what they mean. We also talk briefly about all the laws of gas, but discuss at length Boyle`s law and its mathematical expression, as the title of the topic suggests. Towards the end, we discuss some frequently asked questions and quickly review the whole topic in the last part.
Experiments and observations in physics have led to the development of four fundamental principles that describe the behavior of gases: Boyle`s law, Karl`s law, Avagadro`s law and Gay-Lussac`s law. The experiences and observations described in this section have led to the development of gas laws. These laws are very useful to explain the behavior of gases under constant pressure and temperature. We discussed Boyle`s law and its mathematical expression P1V1 = P2V2 in more detail. Boyle`s Law is often used as part of an explanation of how the respiratory system works in the human body. This often involves explaining how lung volume can be increased or decreased, causing relatively lower or higher air pressure (in accordance with Boyle`s Law). This forms a pressure difference between the air in the lungs and the ambient air pressure, which in turn triggers inhalation or exhalation as the air changes from high to low pressure. [15] This relationship between pressure and volume was first established by Richard Towneley and Henry Power in the 17th century. [4] [5] Robert Boyle confirmed their discovery through experiments and published the results. [6] According to Robert Gunther and other authorities, it was Boyle`s assistant, Robert Hooke, who built the experimental apparatus. Boyle`s law is based on experiments with air, which he considered to be a liquid of particles resting between small, invisible sources.
At the time, tune was still considered one of the four elements, but Boyle disagreed. Boyle`s interest was probably to understand air as an essential element of life; [7] He has published work on the growth of airless plants. [8] Boyle used a closed J-shaped tube, and after pouring mercury on one side, he forced the air on the other side to contract under the pressure of mercury. After repeating the experiment several times and using varying amounts of mercury, he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume it occupies. [9] The French physicist Edme Mariotte (1620-1684) discovered the same law independently of Boyle in 1679,[10] but Boyle had already published it in 1662. [9] However, Mariotte discovered that the volume of air changes with temperature. [11] Therefore, this law is sometimes referred to as the Mariotte law or the Boyle-Mariotte law. Later, in 1687, in the Philosophiæ Naturalis Principia Mathematica, Newton showed mathematically that in an elastic fluid composed of stationary particles between which the repulsive forces are inversely proportional to their distance, the density would be directly proportional to the pressure,[12] but this mathematical treatise is not the physical explanation of the observed relationship. Instead of a static theory, a kinetic theory is needed, provided two centuries later by Maxwell and Boltzmann. This equation can be used to predict the increase in pressure that a gas exerts on the walls of its tank when the volume of its tank is reduced (and its quantity and absolute temperature remain unchanged).
This equation shows that as the volume increases, the gas pressure decreases proportionately. Similarly, as the volume decreases, the gas pressure increases. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. [3] Answer: If you increase the pressure on a certain volume of gas, the number of gas molecules in that volume also increases, and the volume is said to have increased in response to the increase in pressure. Daniel Bernoulli (1737-1738) derived Boyle`s law by applying Newton`s laws of motion at the molecular level. It remained ignored until about 1845, when John Waterston published a paper constructing the great principles of kinetic theory; this was rejected by the Royal Society of England. Later work by James Prescott Joule, Rudolf Clausius and especially Ludwig Boltzmann established the kinetic theory of gases and drew attention to the two theories of Bernoulli and Waterston. [14] Boyle`s law, also called Mariotte`s law, a relation to the compression and expansion of a gas at constant temperature. This empirical relationship, formulated by physicist Robert Boyle in 1662, states that the pressure (p) of a given quantity of gas varies inversely with its volume (v) at constant temperature; that is, in the form of an equation pv = k, a constant.
The relationship was also discovered by the French physicist Edme Mariotte (1676). where P is the pressure of the system, V is the volume of the gas, k is a constant value representative of the temperature and volume of the system. The pressure/s volume curve for a fixed quantity of gas maintained at a constant temperature is shown below. Charle`s law, which is a law of gas, states that in perfect gas mixtures, the pressure is inversely proportional to the volume of a gas. The law is named after chemist Robert Charles (Charles) Lilienfeld, who first published it in 1847. Charles` Law is important in several areas of science, including astronomy, aviation, chemistry, and chemistry. To satisfy Karl`s law, the density of the gas must be constant. where P is the pressure exerted by the gas and V is the volume it occupies. This proportionality can be converted into an equation by adding a constant k. A gas exerts a pressure of 3 kPa on the walls of container 1. If tank 1 is emptied into a 10 litre container, the gas pressure rises to 6 kPa. Find container volume 1.
Suppose the temperature and amount of gas remain constant. When a diver rises rapidly from a deep area to the surface of the water, the pressure drop can cause gas molecules in their body to expand. These gas bubbles can damage the diver`s organs and lead to death. This expansion of the gas, caused by the diver`s ascent, is another example of Boyle`s Law. Another similar example can be seen in deep-sea fish that die after reaching the surface of the water (due to the expansion of gases dissolved in their blood).