Write ideal gas equation. Write the symbolical meaning
Answers
Answer:
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law.[1] The ideal gas law is often written in an empirical form:
Isotherms of an ideal gas. The curved lines represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram) represent higher temperatures.
{\displaystyle PV=nRT}PV=nRT
where {\displaystyle P}P, {\displaystyle V}V and {\displaystyle T}T are the pressure, volume and temperature; {\displaystyle n}n is the amount of substance; and {\displaystyle R}R is the ideal gas constant. It is the same for all gases. It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently) by August Krönig in 1856[2] and Rudolf Clausius in 1857.[3]
Equation Edit
Molecular collisions within a closed container (the propane tank) are shown (right). The arrows represent the random motions and collisions of these molecules. The pressure and temperature of the gas are directly proportional: as the temperature is increased, the pressure of the propane increases by the same factor. A simple consequence of this proportionality is that on a hot summer day, the propane tank pressure will be elevated, and thus propane tanks must be rated to withstand such increases in pressure.
The state of an amount of gas is determined by its pressure, volume, and temperature. The modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature: the appropriate SI unit is the kelvin.[4]
Common forms Edit
The most frequently introduced forms are:
{\displaystyle pV=nRT=nk_{\text{B}}N_{\text{A}}T,}{\displaystyle pV=nRT=nk_{\text{B}}N_{\text{A}}T,}
where:
{\displaystyle p}p is the pressure of the gas,
{\displaystyle V}V is the volume of the gas,
{\displaystyle n}n is the amount of substance of gas (also known as number of moles),
{\displaystyle R}R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,
{\displaystyle k_{\text{B}}}k_{\text{B}} is the Boltzmann constant
{\displaystyle N_{A}}N_{{A}} is the Avogadro constant
{\displaystyle T}T is the absolute temperature of the gas.
In SI units, p is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins (the Kelvin scale is a shifted Celsius scale, where 0.00 K = −273.15 °C, the lowest possible temperature). R has the value 8.314 J/(K·mol) ≈ 2 cal/(K·mol), or 0.0821 L·atm/(mol·K).
Molar form Edit
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount (n) (in moles) is equal to total mass of the gas (m) (in kilograms) divided by the molar mass (M) (in kilograms per mole):
{\displaystyle n={\frac {m}{M}}.}{\displaystyle n={\frac {m}{M}}.}
By replacing n with m/M and subsequently introducing density ρ = m/V, we get:
{\displaystyle pV={\frac {m}{M}}RT}{\displaystyle pV={\frac {m}{M}}RT}
{\displaystyle p={\frac {m}{V}}{\frac {RT}{M}}}{\displaystyle p={\frac {m}{V}}{\frac {RT}{M}}}
{\displaystyle p=\rho {\frac {R}{M}}T}{\displaystyle p=\rho {\frac {R}{M}}T}
Defining the specific gas constant Rspecific(r) as the ratio R/M,
{\displaystyle p=\rho R_{\text{specific}}T}{\displaystyle p=\rho R_{\text{specific}}T}
This form of the ideal gas law is very useful because it links pressure, density, and temperature in a unique formula independent of the quantity of the considered gas. Alternatively, the law may be written in terms of the specific volume v, the reciprocal of density, as
{\displaystyle pv=R_{\text{specific}}T.}{\displaystyle pv=R_{\text{specific}}T.}
It is common, especially in engineering and meteorological applications, to represent the specific gas constant by the symbol R. In such cases, the universal gas constant is usually given a different symbol such as {\displaystyle {\bar {R}}}{\displaystyle {\bar {R}}} or {\displaystyle R^{*}}R^{*} to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to.[5]
Answer:
An ideal gas assumes the particles are point-like compared to the volume of the container and experience elastic collisions with each other and the walls of the container. Real gases aren't perfectly ideal but are modelled to a good approximation using the ideal gas law for high temperature, low pressure gases.
1a : using, employing, or exhibiting a symbol. b : consisting of or proceeding by means of symbols. 2 : of, relating to, or constituting a symbol. 3 : characterized by or terminating in symbols symbolic thinking. 4 : characterized by symbolism a symbolic dance.
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