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B.3: gas laws - Coggle Diagram
B.3: gas laws
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The kinetic theory of gases provides a model to explain the behavior of ideal gases. Ideal gases are hypothetical gases whose behavior is approximated by a set of assumptions that allow us to predict their macroscopic properties such as pressure, temperature, and volume.
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Gas molecules are in constant, random motion. The gas molecules move in straight lines until they collide with other molecules or the walls of the container.
Collisions between gas molecules are perfectly elastic. This means there is no net loss of energy when gas molecules collide with each other or with the walls of the container. The total kinetic energy of the gas molecules remains constant.
Gas molecules are point particles. In the ideal gas model, the size of the molecules is negligible compared to the distance between them. This assumption simplifies calculations and ignores the effects of intermolecular forces.
No intermolecular forces exist between the gas molecules. The model assumes that gas molecules do not attract or repel each other, meaning the only interactions are elastic collisions.
Using these assumptions, the kinetic theory provides relationships between the microscopic properties (such as the velocities and energies of gas molecules) and macroscopic properties (such as pressure and temperature). One key result from the kinetic theory is the ideal gas law.
The ideal gas law is a fundamental equation relating pressure, volume, and temperature of an ideal gas:PV= nRT
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Pressure is a fundamental physical quantity that describes the force applied perpendicular to a surface per unit area. It's mathematically expressed as: P= F/A
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P is pressure (measured in Pascals, Pa)
F is force (measured in Newtons, N)
A is area (measured in square meters, m²)
The amount of substance n in terms of the number of particles (atoms, molecules, ions, etc.) is given by:
where is the total number of particles in the sample and is the Avogadro constant (approximately particles per mole). This gives the amount of substance in moles, and one mole of any substance contains the same number of particles.
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Pressure in gases arises from the momentum change of particles during collisions with the walls of their container.
According to the kinetic theory of gases, the pressure exerted by a gas is related to the rate at which gas molecules collide with the container walls.
The change in momentum during each collision is directly related to the velocity of the particles, and this momentum transfer gives rise to the macroscopic pressure observed in the gas.
The pressure of an ideal gas is related to the average translational speed of its molecules:P=1/3 pv^2
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Average kinetic energy
From the kinetic theory, the pressure exerted by a gas is directly proportional to the number of molecules and their average kinetic energy. The temperature of the gas is a measure of the average kinetic energy of the molecules
This relationship shows that temperature is directly related to the kinetic energy of the molecules in the gas. As temperature increases, the molecules move faster, leading to more frequent and more energetic collisions with the container walls, thus increasing the pressure.
Internal Energy of an Ideal Monatomic Gas
The internal energy (U) of an ideal gas is the total energy associated with the motion of its particles. For a monatomic ideal gas, this energy consists solely of the kinetic energy of the molecules. The internal energy is proportional to the temperature, and for a monatomic ideal gas, it can be calculated as:
U=3/2NKbT or 3/2nRT