Mariotte's Law, Boyle-Mariotte's Law, gas physics, Robert Boyle, Edme Mariotte, volume, pressure, temperature, Newton's second law, fundamental law of dynamics, force, mass, acceleration, gas behavior, thermodynamics, gas chemistry, pressure systems, helium balloon, altitude ascension, temperature variations, atmospheric pressure, gas volume, newtons, kilograms, meters per second squared, P1V1=P2V2, inverse proportionality, scientific principles, engineering applications, energy production, meteorology, medicine, gas confinement systems, atmospheric conditions, pressure decrease with altitude, vector representation of forces, weight calculation, dynamics verification, acceleration calculation, mass conversion to kilograms, Mariotte's Law formula, V0 Patm sol = Vh Ph, gas laws, physical principles, scientific applications.
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Abstract
This document discusses Mariotte's Law, also known as Boyle-Mariotte's Law, and its application to gas behavior at varying altitudes and temperatures.
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[...] It allows for the prediction of gas behavior under different conditions and has practical applications in fields as diverse as energy production, meteorology, medicine, and many others. The Mariotte's law is therefore a valuable tool to understand and manipulate the behavior of gases in various contexts, and it remains a fundamental pillar of gas physics. 2.3. Initial volume of the balloon V0 = 4.0 m3 ; Patm sol = hPa. Let us write the Mariotte's law: [...]
[...] By graphical reading, we get an altitude of 17 km. 2.4. In the specific context of altitude ascension with a balloon, the validity of Mariotte's law can be questioned due to the temperature variations encountered. Indeed, Mariotte's law, which describes the relationship between the volume and pressure of a gas at constant temperature, can only be applied rigorously if the temperature remains stable. In your case, the temperature decreases significantly with altitude. At an altitude of 30 km, the temperature is recorded at -35 °C, while at ground level, it was approximately 26 °C. [...]
[...] Now, let's calculate the weight P of the system studied. We use the formula P=m×g where g=9.81m/s² is the acceleration due to gravity. Thus, P=4.62×9.81=45.3N 1.3. To represent the forces acting on the system, represented by a point mass noted we refer to the figure below. 1.4. From there, we can deduce the vector representing the sum of the forces applied to the system. The characteristics of this vector include its direction, sense, and norm. The sum vector of forces is vertical, oriented upwards, with a norm of 50-45.3 = 4.7 N. [...]
[...] Mathematically, it is formulated as follows: F=m×a Where : - F represents the net force acting on the object (expressed in newtons, - m represents the mass of the object (expressed in kilograms, and - a represents the acceleration of the object (expressed in meters per second squared, m/s²). This law expresses the fundamental link between the force, mass, and acceleration of an object. It is essential to understand the movement of objects and is one of the cornerstones of classical mechanics. 2. Explosion. 2.1. Upon observing the graph, it is observed that atmospheric pressure decreases as altitude increases. 2.2. [...]
