 # Ideal Gas definition and properties

## How to calculate the pressure, volume, density of an ideal gas ?

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1. Ideal Gas Law
2. Molar volume of an ideal gas Vm
3. Mass and volume flow rate correction
4. Volume flow rates corrections
5. Specific heats

## 1. Ideal Gas law

### Perfect Gas law / Avogadro Law

The ideal gas law allows to represent the behavior of gases at low pressure. In order to reach a simple form, It takes the assumption that there is no interaction in between the molecules of the gas.

PV = nRT

With
P = absolute pressure of the gas
V = volume of the gas
n = quantity of the gas (in moles)
T = absolute temperature of the gas
R = perfect gas constant

In SI, P is in Pa abs, V is in m3, n is in moles, T is in K and R = 8.314

In US units, P is in PSI abs, V in ft3, n in lbmoles, T is in R, R = 10.73

Note that this expression can also be used with flow rates of gas.

Changes to ideality

The ideal gas law has often be used as a starting point for other equation of states allowing to introduce correction factors to better represent the behavior of gases at higher pressure

## 2. Molar volume of an ideal gas Vm

The molar volumes of an ideal gas can be calculated from the ideal gas law

PV = nRT

V/n = RT/P

Vm = RT/P

With :

Vm = molar volume in m3/kmol
T = temperature in K
P = pressure in Pa abs
R = ideal gas constant

The molar volume of an ideal gas in normal conditions is 22.4 l/mol, the normal conditions being T = 0°c, P = 101325 Pa.

## 3. Mass and volume flow rate conversions

It is possible to convert gas mass to volume flowrate, volume to mass flowrate thanks to the ideal gas law.

Qm = Qv

Qv = Qm / ρ

Qv = Qm . RT/PM

With :
Qm = mass flowrate in kg/h
Qv = volume flowrate in m3/h
M = molecular weight of the gas in g/mol
P = pressure absolute in Pa abs
T = temperature in K
R = 8.314

## 4. Volume flow rates correction

The volume of a gas in changing depending on the conditions, as gases are compressible. Knowing the volume in condition 1, it is often required to calculate the new volume in condition 2 following a change of pressure or temperature. It is typically what happens along a pipe, where the pressure is changing due to the pressure drop along the pipe and the gas is expanding. If there is no gain or loss of material, the ratio Qv.P/T remains constant.

Qv1.P1/T1 = Qv2.P2/T2

Qv2 = Qv1.T2/T1.P1/P2 With

Qv1 : volumetric flow rate at condition 1 in m3/h
Qv2 : volumetric flow rate at condition 2 in m3/h
P1 : pressure at condition 1 in Pa
P2 : pressure at condition 2 in Pa
T1 : temperature at condition 1 in K
T2 : temperature at condition 2 in K

Particular case of normal conditions

When performing some calculations with gas, it happens very often that the flow of gas is expressed in Nm3/h, referring to normal conditions. In this case the formula above can be expressed the following way :

Qvn = Qv*273/T*P/1.013

Qv = Qvn*T/273*1.1013/P With

Normal conditions : t = 273K and P = 1.013 bar abs
Qvn : volumetric flow rate at normal conditions in Nm3/h
Qv : volumetric flow rate at condition studied in m3/h
P : pressure at condition studied in bar abs
T : temperature at condition studied in K

## 5. Specific heat of ideal gas

The specific heat at constant pressure of an ideal gas can often be represented through the following form :

Cp = a + bT + cT2 + dT3

The coefficients can be found in tables.

Another specific heat, at constant volume, can be determined for a substance. For an ideal gas, the relations in between the specific heat at constant pressure and at constant volume is given by the following relations :

Cp/Cv = k

If Cp and Cv are in kcal / kmol.K, R = 1.987 kcal/kmol.K :

Cp - Cv = R

k = Cp/(Cp - R)

If Cp and Cv are in kcal / kg.K, R = 8.314 kJ/kmol.K

Cp - Cv = R/M

k =Cp/(Cp - R/M)

k is the isentropic coefficient of ideal gas.