The Equation-Of State of An Ideal Gas Is Found To Be

Ideal Gases
Ideal gases are defined as having molecules of negligible size with an average molar
kinetic energy dependent only on temperature. At a low temperature, most gases behave
enough like ideal gases that the ideal gas law can be applied to them. An ideal gas is also known
as a perfect gas.
Equation of State
The equation-of state of an ideal gas is found to be:
PV = nRT
,where
P = pressure
V = volume
T = absolute temperature
n = no. of moles of gas (= mass/molar mass)
R = universal gas constant (8.314 J mol-1 K-1
Note: Mole is a counting unit, where one mole = 6.022 x 1023 particles.
P, V, and T are the thermodynamic variables of the gas.
The behaviour of real gases at not-too-high pressures and at not-too-low temperature

is very well described by this ideal gas equation.
Another form of ideal gas law
The ideal gas law can also be expressed in number of gas particles N (instead of the
number of moles of gas particles n).
PV = NkBT
,where
P = pressure
V = volume
T = absolute temperature
N = number of gas molecules (i.e., number of molecules)
kB = Boltzmann’s constant (1.381 x 10-23 J K-1
Note:
R = NAkB, where NA is the Avogadro’s constant (6.022 x 1023)
Ideal Gas Law
An ideal gas is a gas that conforms, in physical behaviour, to a particular, idealized

relation between pressure, volume, and temperature called the ideal gas law. This law
is a generalization containing both Boyle's law and Charles's law as special cases and
states that for a specified quantity of gas, the product of the volume, V, and pressure,
P, is proportional to the absolute temperature T; i.e., in equation form, PV = kT, in
which k is a constant. Such a relation for a substance is called its equation of state and
is sufficient to describe its gross behaviour.
The ideal gas law can be derived from the kinetic theory of gases and relies on the
assumptions that (1) the gas consists of a large number of molecules, which are in
random motion and obey Newton's laws of motion; (2) the volume of the molecules is
negligibly small compared to the volume occupied by the gas; and (3) no forces act on
the molecules except during elastic collisions of negligible duration.
Although no gas has these properties, the behaviour of real gases is described quite
closely by the ideal gas law at sufficiently high temperatures and low pressures, when
relatively large distances between molecules and their high speeds overcome any
interaction. A gas does not obey the equation when conditions are such that the gas, or
any of the component gases in a mixture, is near its condensation point.
The ideal gas law may be written in a form applicable to any gas, according to
Avogadro's law (q.v.), if the constant specifying the quantity of gas is expressed in
terms of the number of molecules of gas. This is done by using as the mass unit the
gram-mole; i.e., the molecular weight expressed in grams. The equation of state of n
gram-moles of a perfect gas can then be written as pv/t = nR, in which R is called the
universal gas constant. This constant has been measured for various gases under
nearly ideal conditions of high temperatures and low pressures, and it is found to have
the same value for all gases: R = 8.314 joules per gram-mole-kelvin.
Gas Constant
The ideal gas constant is a Universal constant that we use to quantify the relationship between the
properties of a gas. The constant RR that we typically use relates pressure in atmospheres, volume
in liters, and temperature in Kelvin. In this case, it has the value and units of
R=0.08206Latmmol−1K−1R=0.08206Latmmol−1K−1
The gas constant RR will appear in many contexts as this is a Universal constant that relates energy
and temperature. A pressure times a volume is an energy. As such, you will also encounter the gas
constant RR in typical energy units of Joules
R=8.314Jmol−1K−1
Specific Heat
All ideal gases:
1. The specific heat at constant volume ( for a unit mass or for one
kmol) is a function of only.
2. The specific heat at constant pressure ( for a unit mass or for one
kmol) is a function of only.
3. A relation that connects the specific heats , , and the gas constant
is
where the units depend on the mass considered. For a unit mass of
gas, e.g., a kilogram, and would be the specific heats for one
kilogram of gas and is as defined above. For one kmol of gas, the
expression takes the form
where and have been used to denote the specific heats for one
kmol of gas and is the universal gas constant.
4. The specific heat ratio, (or ), is a function of only
and is greater than unity.

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Ideal Gases

The equation-of state of an ideal gas is found to be:

P, V, and T are the thermodynamic variables of the gas.

The behaviour of real gases at not-too-high pressures and at not-too-low temperature

Another form of ideal gas law

Ideal Gas Law

An ideal gas is a gas that conforms, in physical behaviour, to a particular, idealized

All ideal gases:

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