Isotherms of an ideal gas

The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. Image File history File links Download high resolution version (1504x1386, 66 KB)Isotherms of an ideal gas in pressure (p) vs. ... Image File history File links Download high resolution version (1504x1386, 66 KB)Isotherms of an ideal gas in pressure (p) vs. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ... In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... Benoit Paul Émile Clapeyron Benoît Paul Émile Clapeyron (February 26, 1799 - January 28, 1864) was a French engineer and physicist, one of the founders of thermodynamics. ... 1834 was a common year starting on Wednesday (see link for calendar). ...

The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:

where In thermodynamics, a state function, or state quantity, is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ... This article or section does not adequately cite its references or sources. ...

is the absolute pressure [Pa],

is the volume [m³],

is the amount of substance of gas [mol],

is the gas constant 8.3143 m³·Pa·K^-1·mol^-1, and

is the temperature in kelvin [K].

The ideal gas constant (R) is dependent on what units are used in the formula. The value given above, 8.314472, is for the SI units of pascal-cubic meters per mole-kelvin. Another value for R is 0.082057 L atm mol^-1 K^-1) The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... Amount of substance of an object is a physical quantity that measures the number of elementary entities in the object compared with the number of elementary entities in 0. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... Fig. ... The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero—the lowest possible temperature where nothing could be colder and no heat energy remains in a substance—is defined as zero kelvin (0 K). ... Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ... Cover of brochure The International System of Units. ... The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero—the lowest possible temperature where nothing could be colder and no heat energy remains in a substance—is defined as zero kelvin (0 K). ...

The ideal gas law is the most accurate for monatomic gases and is favored at high temperatures and low pressures.^{[citation needed]} It does not factor in the size of each gas molecule or the effects of intermolecular attraction. The more accurate Van der Waals equation takes these into consideration. The van der Waals equation is an equation of state for a fluid composed of particles that have a non-zero size and a pairwise attractive inter-particle force (such as the van der Waals force. ...

Ideal gas law mathematically follows from statistical mechanics of primitive identical particles (=particles without internal structure) when the only interaction between them is exchange of momentum and kinetic energy in elastic collisions. Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... In classical mechanics, momentum (pl. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. ...

Alternate forms

Considering that the number of moles (n) could also be given in mass, sometimes you may wish to use an alternate form of the ideal gas law. This is particularly useful when asked for the ideal gas law approximation of a known gas. Consider that the number of moles (n) is equal to the mass (m) divided by the molar mass (M), such that: Molar mass is the mass of one mole of a chemical element or chemical compound. ...

Then, replacing n gives: in statistical mechanics, and is often derived from first principles: Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

Here, k_b is Boltzmann's constant, and N is the actual number of molecules, in contrast to the other formulation, which uses n, the number of moles. This relation implies that Nk_b = nR, and the consistency of this result with experiment is a good check on the principles of statistical mechanics. The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

From here we can notice that for an average particle mass of μ times the atomic mass of Hydrogen,

and since ρ = m / V, we find that the ideal gas law can be re-written as:

Proof

Empirical

The ideal gas law can be proved using Boyle, Charles and Gay-Lussac laws. Boyles law (sometimes referred to as the Boyle Mariotte law) is one of the gas laws. ... The Law of Charles and Gay-Lussac (frequently called simply Charles Law) is one of the gas laws, and relates the volume and temperature of an ideal gas held at a constant pressure. ...

Consider an amount of gas. Let its initial state be defined as:

volume = v₀

pressure = p₀

temperature = t₀

If this gas now undergoes an isobaric process, its state will change: An isobaric process is a thermodynamic process in which the pressure stays constant; . The heat transferred to the system does work but also changes the internal energy of the system: according to the first law of thermodynamics, where W is work done by the system, E is internal energy, and...

volume:

pressure

temperature .

If it then undergoes an isothermal process: An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. ...

where

p = final pressure

v = final volume

T = final temperature (= t')

So:

;

where

, termed R, is the universal gas constant.

Using this notation we get: Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ...

And multiplying both sides of the equation by n (numbers of moles): The mole (symbol: mol) is the SI base unit that measures an amount of substance. ...

Using the symbol V as a shorthand for nv (volume of n moles) we get:

Theoretical

The ideal gas law can also be derived from first principles using the kinetic theory of gases, in which several simplifying assumptions are made, chief amongst which is that the molecules, or atoms, of the gas are point masses, possessing mass but no significant volume. In a formal logical system, that is, a set of propositions that are consistent with one another, it is probable that some of the statements can be deduced from one another. ... The kinetic theory of gases is a theory that explains the macroscopic properties of gases by consideration of their composition at a molecular level. ...

See also

• Ideal gas
• Equation of state
• Thermodynamics
• Boyle's Law
• Charles's Law
• Dalton's Law
• Amagat's law

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ... Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Boyles law (sometimes referred to as the Boyle Mariotte law) is one of the gas laws. ... Wikibooks has more about this subject: Constructing school science lab equipment/Making Charles law tubes AARON IS SO COOL!!!!! Charles law (sometimes called the Law of Charles) is one of the gas laws. ... In chemistry and physics, Daltons law (also called Daltons law of partial pressures) states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture. ... In physics, Amagats law (1880) states the volume of a gas mixture is equal to the sum of volumes of two gases, if the temperature and the pressure stays the same. ...

References

• Davis and Masten Principles of Environmental Engineering and Science, McGraw-Hill Companies, Inc. New York (2002) ISBN 0-07-235053-9
• Website giving credit to Benoît Paul Émile Clapeyron, (1799-1864) in 1834
• Website containing Ideal Gas Law Calculator & a host of other scientific calculators, Rex Njoku & Dr. Anthony Steyermark -University of St.Thomas

Benoit Paul Émile Clapeyron Benoît Paul Émile Clapeyron (February 26, 1799 - January 28, 1864) was a French engineer and physicist, one of the founders of thermodynamics. ... 1834 was a common year starting on Wednesday (see link for calendar). ...