# Ideal Gas Law and Ideal Gas State Equation

Ideal gas law is divided into 5 which is avogadro, boyle-mariotte, charles-gay lussac, dalton and amagat law.

**1) Avogadro’s Law:**

A.avogadro 1811, “the same pressure and temperature, all ideal gases has the same number of molecules in equal volumes,” it has put forward the hypothesis that expression and was then known as Avogadro’s law. According to Avogadro’s law, the standard conditions (0 ° C and 101.325 kPa) the volume of all the molecules of an ideal gas occupies 6,022.10 ^{26} units is 22.4 liters. 6,022.10 ^{26} number of Avogadro’s number, also called molar volume of 22.4 liters.

Matter is called mass and molar mass as a mole gram g / mol or kg / kmol is expressed in units. For example molar mass of CO2 gas M = 44 g / mol. The specific volume multiplied by the molar mass Mv = 22.4 m³ / kmol stop. Between two different gas volume and the same conditions of molar number n2 / n1 = V2 / V1 has a correlation. Also mole volume density Vm = M / p depends on the form.

**2) Boyle-Mariotte law:**

R.boyl in 1662 and 1676 in the e.mariot Boyle independent of “the product of the pressure and volume of a gas is heated at a constant temperature is constant” determined the property. This feature is called the Boyle-Mariotte law. PV = constant (T = while fixed)

**3) Charles-Gay Lussac’s Law:**

J.charles and jlgay Lussac in 1802, “the volume of a gas is heated at constant pressure varies linearly with temperature” determined the property. This feature is called Charles-Gay Lussac’s Law.Mathematically V = V0 (1 + αt) position. Where V T is the temperature in the gas volume, Vo: volume of gas at 0 ° C, α: gas volume expansion coefficient (α = 1/273 = 0.00366) is.

for constant pressure, V1 and V2, respectively T1 and T2 temperature of the gas volumes, V2 / V1 = T2 / T1 equal writable.

*Sample:*

Temperature 1200 K, the volume of 2 m3 of a gas is heated up to 1800 K temperature at constant pressure. The final volume of the gas would have escaped m3? Solution: V2 / V1 = T2 / T1 from the equation V2 = V1. T2 / T1 = 2. 1800/1200 = has 3 cubic meters.

**4) Dalton’s Law:**

“A gas pressure of the mixture to be in the mix temperature of the forming gas mixtures separately and the total volume of the sum of the pressure they would have had in case of coatings Dalton’s Law” is called. Pkarıar U = Σ Pi (t, V = constant)

**5) Amagat Act:**

“The volume of a gas mixture, if they are in the gas mixture temperature and pressure of the mixture is the sum of the volumes of individual coating” it means as known Amagat Law. Vkarıar U = Σ V (T, P = constant)

## Ideal Gas Equation of State

The pressure of a substance, that the relationship between temperature and volume of any specific relation to the equation of state is given a name.

Ideally located by using the equation of state of the law Boyle-Mariotte and Gay-Lussac’s law Charles for gas. P1.V1 / T1 = P2.V2 / T2 = constant, this constant is called the gas constant and denoted by R. Pv = RT equality Clapeyron equation, or known as the ideal gas equation of state. v = V / m is the ideal gas equation can be written as PV = MRT.

R is where R = R / M = (8.3143) / M shaped. Where M is the molecular mass of gas (kg / kmol). R = 8.3143 kJ / kmol if the value is called the universal gas constant and the same for all gases. Any mass of a gas is equal to the product of the number of moles of molecular weight by, m = nm depending on the number of moles of the ideal gas equation in this case; It can be written as PV = n.ru.t.

*Sample:*

CO2 gas passes through a tube diameter of 30 cm. The pressure of the gas in the pipe at 275 kPa, 500 K temperature, speed of 60 m / s to be, the mass flow rate;

a) kg / s, b) kmol / h Calculate. (Π = 3.14, M = 44 kg / kmol)

*Solution:*

a) PV = MRT

V = AC = π. (0.15) ² .60 = 4,241 m / s,

R = R / M = (8.3143) / 44 = 0.189 kJ / UPS

m = PV / RT = 275. (4.241) / (0.189) .500 = 12.344 kg / h

b) n = m / M = 7.75 / 36.14 = 0.28056 kmol / s are present.

Source: Mehmet TAŞKAN, Ideal Gas Law