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Section summary |
---|

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 |

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

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

PV = nRT

V/n = RT/P

**V _{m}
= RT/P**

With :

V_{m} =
molar volume in m^{3}/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.

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

**Q _{m} = Q_{v}.ρ**

Q_{v} = Q_{m} / ρ

**Q _{v} = Q_{m} .
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

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.

Qv_{1}.P_{1}/T_{1}
= Qv_{2}.P_{2}/T_{2}

Qv_{2} = Qv_{1}.T_{2}/T_{1}.P_{1}/P_{2}

With

Qv_{1} : volumetric flow rate at condition 1 in m3/h

Qv_{2} : volumetric flow rate at condition 2 in m3/h

P_{1} : pressure at condition 1 in Pa

P_{2} : pressure at condition 2 in Pa

T_{1} : temperature at condition 1 in K

T_{2} : 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 :

Q_{vn} = Q_{v}*273/T*P/1.013

Q_{v} = Qv_{n}*T/273*1.1013/P

With

Normal conditions : t = 273K and P = 1.013 bar abs

Qv_{n} : volumetric flow rate at normal conditions in Nm3/h

Q_{v} : volumetric flow rate at condition studied in m3/h

P : pressure at condition studied in bar abs

T : temperature at condition studied in K

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.