6 min read•Last Updated on July 30, 2024
Gas behavior is crucial in thermodynamics. The ideal gas equation simplifies calculations, assuming negligible particle volume and no intermolecular forces. It's most accurate at low pressures and high temperatures, providing a foundation for understanding gas properties.
Real gases deviate from ideal behavior, especially at high pressures or low temperatures. Other equations of state, like van der Waals or Redlich-Kwong, account for these deviations. Choosing the right equation depends on the gas, conditions, and required accuracy for specific applications.
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Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law | General Chemistry View original
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2.1 Molecular Model of an Ideal Gas – University Physics Volume 2 View original
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Ideal Gas Law | Boundless Physics View original
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Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law | General Chemistry View original
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An adiabatic process is a thermodynamic process in which no heat is transferred into or out of the system. During this type of process, any change in the internal energy of the system is solely due to work done on or by the system, making it essential in understanding how systems behave under different conditions.
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An adiabatic process is a thermodynamic process in which no heat is transferred into or out of the system. During this type of process, any change in the internal energy of the system is solely due to work done on or by the system, making it essential in understanding how systems behave under different conditions.
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The ideal gas equation is a mathematical relationship that describes the behavior of an ideal gas, expressed as $$PV=nRT$$, where $$P$$ is pressure, $$V$$ is volume, $$n$$ is the number of moles, $$R$$ is the universal gas constant, and $$T$$ is temperature in Kelvin. This equation connects various properties of gases and serves as a foundational concept in thermodynamics, enabling the exploration of how gases behave under different conditions, as well as the calculation of other thermodynamic properties.
Universal Gas Constant: The constant $$R$$ that appears in the ideal gas equation, with a value of approximately 8.314 J/(mol·K), representing the relationship between energy, temperature, and amount of substance.
Real Gas: Gases that do not perfectly follow the ideal gas equation due to intermolecular forces and the volume occupied by gas molecules, often requiring adjustments to account for these behaviors.
Boyle's Law: A gas law stating that the pressure of a given mass of gas is inversely proportional to its volume at constant temperature, which can be derived from the ideal gas equation.
Volume is the amount of space occupied by a substance, typically measured in cubic units. It plays a crucial role in understanding the physical properties of matter, the state of a system, and the equilibrium conditions. Knowing the volume helps in analyzing gas behavior, calculating densities, and applying equations of state that describe how substances behave under varying conditions.
Pressure: The force exerted per unit area by the particles of a substance, which influences how volume changes under different conditions.
Density: The mass of a substance per unit volume, providing insight into how tightly packed the matter is within a given space.
State Function: A property that depends only on the current state of a system and not on how it got there, with volume being one such example.
Elastic collisions are interactions between two or more objects where both momentum and kinetic energy are conserved before and after the collision. This type of collision occurs in ideal conditions, such as between gas molecules, where they bounce off each other without losing energy to deformation or heat. The behavior of elastic collisions is crucial for understanding the dynamics of gases and plays a significant role in deriving the ideal gas equation and other equations of state.
Momentum: A vector quantity defined as the product of an object's mass and its velocity, representing the motion of an object.
Kinetic Energy: The energy that an object possesses due to its motion, calculated as $$KE = \frac{1}{2}mv^2$$, where m is mass and v is velocity.
Inelastic Collisions: Collisions in which momentum is conserved, but kinetic energy is not, resulting in some energy being converted to other forms like heat or sound.
The kinetic theory of gases is a scientific model that explains the behavior of ideal gases by considering the motion of individual molecules. It posits that gas consists of a large number of small particles (atoms or molecules) that are in constant random motion and that their collisions with each other and the walls of their container are perfectly elastic. This theory connects to the ideal gas equation and other equations of state, providing insights into how temperature, pressure, and volume relate to the microscopic behavior of gas particles.
Ideal Gas: A hypothetical gas that perfectly follows the ideal gas law, where interactions between molecules are negligible and they occupy no volume.
Elastic Collision: A type of collision in which there is no net loss of total kinetic energy in the system, meaning that the total kinetic energy before and after the collision remains constant.
Pressure: The force exerted by gas particles when they collide with the walls of their container, related to the number of collisions and the energy of the particles.
Temperature is a measure of the average kinetic energy of the particles in a substance, providing an indication of how hot or cold that substance is. It plays a critical role in understanding properties, state changes, and equilibrium conditions of substances, influencing how they interact with one another and their environments.
Thermal Equilibrium: A state in which two objects in contact do not exchange heat, meaning they are at the same temperature.
Absolute Zero: The theoretical temperature at which all particle motion ceases, defined as 0 Kelvin or -273.15°C.
Heat Transfer: The process of energy moving from one object or system to another due to a temperature difference.
Pressure is defined as the force exerted per unit area on the surface of an object. It plays a crucial role in understanding the behavior of substances in various states, how systems reach equilibrium, and is a key parameter in equations that describe the relationships between different properties of gases and fluids.
Absolute Pressure: Absolute pressure is the pressure measured relative to a perfect vacuum, representing the total pressure exerted on a system without considering atmospheric pressure.
Gauge Pressure: Gauge pressure is the pressure relative to atmospheric pressure, indicating how much pressure is exerted above atmospheric levels.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it, commonly observed in fluids at different depths.
Density is defined as the mass of a substance per unit volume, typically expressed in units such as kg/m³ or g/cm³. This concept is crucial for understanding how substances behave under various conditions and is particularly important when dealing with gases, liquids, and mixtures. Density helps in identifying whether a substance will float or sink, and it plays a significant role in calculating other properties like pressure and temperature relationships in different states of matter.
Specific Gravity: The ratio of the density of a substance to the density of a reference substance, usually water for liquids and air for gases.
Molar Mass: The mass of one mole of a substance, which can be used to determine the density of gases when combined with the ideal gas law.
Buoyancy: The upward force exerted by a fluid that opposes the weight of an object immersed in it, directly related to the densities of the object and the fluid.
Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It provides a bridge between the atomic scale and macroscopic quantities, allowing chemists to convert between the mass of a substance and the number of particles it contains. In the context of ideal gas behavior and gas mixtures, molar mass plays a critical role in calculations involving the ideal gas equation and the properties of gas mixtures, affecting their density and composition.
Mole: A mole is a unit that measures the amount of substance, defined as containing exactly 6.022 × 10²³ particles, be it atoms, molecules, or ions.
Density: Density is the mass per unit volume of a substance, typically expressed in grams per liter (g/L) for gases, which is influenced by molar mass.
Ideal Gas Law: The Ideal Gas Law is an equation of state for an ideal gas, represented as PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature.
The van der Waals equation is a modified version of the ideal gas law that accounts for the volume occupied by gas molecules and the intermolecular forces present in real gases. It introduces two constants, 'a' and 'b', which correct for the attractive forces between particles and the finite size of the particles themselves, thus providing a more accurate representation of gas behavior under various conditions.
Ideal Gas Law: A fundamental equation in thermodynamics given by PV=nRT, describing the behavior of an ideal gas where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
Real Gas: A gas that does not behave ideally and exhibits interactions between molecules, particularly at high pressures and low temperatures, necessitating adjustments like those made in the van der Waals equation.
Critical Point: The temperature and pressure at which the properties of a gas and liquid phase become indistinguishable, beyond which distinct liquid and gas phases do not exist.
The Redlich-Kwong equation is an empirical equation of state that describes the behavior of real gases, particularly at high pressures and temperatures. It modifies the ideal gas law by introducing a volume correction term and an attraction parameter to better account for the interactions between gas molecules, making it more accurate for real gas applications compared to simpler models like the ideal gas equation.
Ideal Gas Law: A fundamental equation that relates the pressure, volume, and temperature of an ideal gas, expressed as PV=nRT, where n is the number of moles and R is the universal gas constant.
Van der Waals Equation: An equation of state that adjusts the ideal gas law by incorporating parameters for molecular size and intermolecular forces, enabling better predictions of real gas behavior.
Compressibility Factor: A factor that quantifies how much a real gas deviates from ideal behavior, calculated as the ratio of the molar volume of a real gas to the molar volume predicted by the ideal gas law.
The Soave-Redlich-Kwong (SRK) equation is an improved equation of state derived from the original Redlich-Kwong equation, designed to better predict the behavior of real gases, particularly near their critical points. It incorporates a temperature-dependent parameter to account for the attractive forces between molecules, making it more accurate for non-ideal gas behavior compared to the ideal gas equation and other equations of state.
Redlich-Kwong Equation: An early cubic equation of state that models the behavior of gases by relating pressure, volume, and temperature, though it may not accurately predict phase behavior at high pressures.
Cubic Equations of State: A class of equations of state that relate pressure, volume, and temperature using cubic polynomial forms, often used for predicting gas and liquid phase behavior.
Critical Point: The specific temperature and pressure at which a substance's gas and liquid phases become indistinguishable, marking a transition into a supercritical fluid.
The Peng-Robinson equation is an empirical equation of state that describes the behavior of real gases, especially in the context of phase equilibria. This equation improves upon the ideal gas law by accounting for the effects of molecular interactions and finite molecular volume, making it particularly useful for predicting the properties of hydrocarbons and other non-ideal gases under various conditions of temperature and pressure.
Ideal Gas Law: A simplified equation that relates pressure, volume, temperature, and the number of moles of an ideal gas, expressed as PV = nRT.
Van der Waals Equation: An early equation of state that modifies the ideal gas law to include the volume occupied by gas particles and the attractive forces between them.
Compressibility Factor: A factor that corrects the ideal gas law to account for deviations from ideal behavior in real gases, represented as Z = PV/RT.
Virial equations of state describe the relationship between pressure, volume, and temperature for real gases by incorporating a series expansion based on the interactions between molecules. These equations extend the ideal gas law by introducing virial coefficients that account for non-ideal behavior, especially at high pressures and low temperatures, where molecular interactions become significant. The virial expansion provides insights into how real gases deviate from ideal behavior and can be used to model various gas behaviors under different conditions.
Ideal Gas Law: A fundamental equation stating that the pressure, volume, and temperature of an ideal gas are related through the equation PV = nRT.
Virial Coefficient: Constants in the virial equation that quantify the effects of intermolecular forces and molecular sizes on the behavior of gases.
Compressibility Factor: A dimensionless factor that describes how much a real gas deviates from ideal gas behavior, defined as Z = PV/nRT.
The Beattie-Bridgeman equation is a modified version of the ideal gas law that accounts for the effects of intermolecular forces and molecular volume in real gases. This equation is particularly useful for understanding the behavior of gases under high pressures and low temperatures, where deviations from ideal behavior become significant. By incorporating factors that account for the interactions between gas molecules, it provides a more accurate representation of gas properties than the ideal gas equation.
Ideal Gas Law: A fundamental equation in thermodynamics that relates pressure, volume, temperature, and number of moles of an ideal gas, represented as PV = nRT.
Van der Waals Equation: An equation of state that describes the behavior of real gases by introducing parameters that account for molecular volume and intermolecular forces.
Compressibility Factor: A dimensionless quantity used to describe how much a real gas deviates from ideal behavior, often denoted as Z = PV/nRT.