Ideal gas law in the context of "Equation of state (cosmology)"

The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small to be seen with a microscope, in constant, random motion. These particles are now known to be the atoms or molecules of the gas. The kinetic theory of gases uses their collisions with each other and with the walls of their container to explain the relationship between the macroscopic properties of gases, such as volume, pressure, and temperature, as well as transport properties such as viscosity, thermal conductivity and mass diffusivity.

The basic version of the model describes an ideal gas. It treats the collisions as perfectly elastic and as the only interaction between the particles, which are additionally assumed to be much smaller than their average distance apart.

In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example. In this law, one state variable (e.g., pressure, volume, temperature, or the amount of substance in a gaseous equilibrium system) is a function of other state variables so is regarded as a state function. A state function could also describe the number of a certain type of atoms or molecules in a gaseous, liquid, or solid form in a heterogeneous or homogeneous mixture, or the amount of energy required to create such a system or change the system into a different equilibrium state.

Internal energy, enthalpy, and entropy are examples of state quantities or state functions because they quantitatively describe an equilibrium state of a thermodynamic system, regardless of how the system has arrived in that state. They are expressed by exact differentials. In contrast, mechanical work and heat are process quantities or path functions because their values depend on a specific "transition" (or "path") between two equilibrium states that a system has taken to reach the final equilibrium state, being expressed by inexact differentials. Exchanged heat (in certain discrete amounts) can be associated with changes of state function such as enthalpy. The description of the system heat exchange is done by a state function, and thus enthalpy changes point to an amount of heat. This can also apply to entropy when heat is compared to temperature. The description breaks down for quantities exhibiting hysteresis.

A hot air balloon is a lighter-than-air aircraft consisting of a bag, called an envelope, which contains heated air. Suspended beneath is a gondola or wicker basket (in some long-distance or high-altitude balloons, a capsule), which carries passengers and a source of heat, in most cases an open flame caused by burning liquid propane. The heated air inside the envelope makes it buoyant, since it has a lower density than the colder air outside the envelope. As with all aircraft, hot air balloons cannot fly beyond the atmosphere. The envelope does not have to be sealed at the bottom, since the air inside the envelope is at about the same pressure as the surrounding air. In modern sport balloons the envelope is generally made from nylon fabric, and the inlet of the balloon (closest to the burner flame) is made from a fire-resistant material such as Nomex. Modern balloons have been made in many shapes, such as rocket ships and the shapes of various commercial products, though the traditional shape is used for most non-commercial and many commercial applications.

The hot air balloon is the first successful human-carrying flight technology. The first untethered manned hot air balloon flight in the world was performed in Paris, France, by Jean-François Pilâtre de Rozier and François Laurent d'Arlandes on November 21, 1783, in a balloon created by the Montgolfier brothers. Hot air balloons that can be propelled through the air rather than simply drifting with the wind are known as thermal airships.

Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The Kelvin scale is defined so that absolute zero is 0 K, equivalent to −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale. The Kelvin and Rankine temperature scales set their zero points at absolute zero by definition. This limit can be estimated by extrapolating the ideal gas law to the temperature at which the volume or pressure of a classical gas becomes zero.

Although absolute zero can be approached, it cannot be reached. Some isentropic processes, such as adiabatic expansion, can lower the system's temperature without relying on a colder medium. Nevertheless, the third law of thermodynamics implies that no physical process can reach absolute zero in a finite number of steps. As a system nears this limit, further reductions in temperature become increasingly difficult, regardless of the cooling method used. In the 21st century, scientists have achieved temperatures below 100 picokelvin (pK). At these low temperatures, matter displays exotic quantum mechanical phenomena such as superconductivity, superfluidity, and Bose–Einstein condensation. The particles still exhibit zero-point energy motion, as mandated by the Heisenberg uncertainty principle and, for a system of fermions, the Pauli exclusion principle.

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.The physical region covered by a system may or may not coincide with a control volume used to analyze the system.

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.

Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Noble gases and mixtures such as air, have a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.71095464... L (exact value based on 2019 revision of the SI) at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 10 Pa).

An electromagnetic catapult is a type of aircraft catapult that uses a linear induction motor system rather than the single-acting pneumatic cylinder (piston) system in conventional steam catapults. The system is used on aircraft carriers to launch fixed-wing carrier-based aircraft, employing the principles of electromagnetism and Lorentz force to accelerate and assist their takeoff from the shorter flight deck runways. Currently, only the United States and China have successfully developed electromagnetic catapults, which are installed on the Gerald R. Ford-class aircraft carriers (currently only the lead ship CVN-78 being operational), the Type 003 aircraft carrier Fujian and the upcoming Type 076 amphibious assault ship Sichuan (51).

Electromagnetic catapults have several advantages over their older, superheated steam-based counterparts. Electromagnetic operation recharges via electric energy and thus much faster than the pressurization process of steam systems, and does not suffer power loss with distance (where volume expansion within the steam catapult cylinder proportionally reduces pressure), temperature changes (which directly affects pressure according to ideal gas law) and leakages (which matters in pressure vessels but is irrelevant in electromagnet systems). The electromagnetic acceleration is also more uniform (unlike steam acceleration, whose accelerative force is always highest at the very initial phase, thus creating a distinct "jolt"), therefore reducing the stress upon the airframe considerably, resulting in increased safety and endurance as well as lower maintenance costs for the aircraft. Electromagnetic catapults are configurable and can assign varying power outputs to different sections, thus allowing them to tailor optimal acceleration to individual aircraft according to different payload weights and takeoff behaviours. Electromagnetic systems are more compact and also weigh less, have fewer linkage components and thus are expected to cost less and require less maintenance, and also require no fresh water boiling for their operation, thus reducing the need for energy-intensive desalination and sophisticated piping systems used in steam catapults, which take up significantly more space below the flight deck.