# Gas Laws & their influence on Natural Gas Flow Measurement

For any natural gas flow measurement instrument to provide accurate gas flow, gas laws must be considered, including Boyle’s Law, Charles’ Law, Avogadro’s Law, Gay-Lussac’s Law, Combined Gas Law, and the Ideal Gas Law. By doing so, we can see how temperature, pressure, and volume impact gas instrumentation.

**Boyle’s Law **

The amount of force pressing on a particular area is known as **pressure** and expressed in various units, such as psi (pounds/inches^{2}), atmospheres, bars, mm of Hg, inches of water, and pascal (Pa).

P Î± 1/V or P_{1}V_{1} = P_{2}V_{2}

Boyle’s Law suggests that when the gas’s temperature is constant, the relationship between a given mass’s pressure (P) is inversely proportional to the volume (V). In other words, if the pressure doubles, the volume is reduced by half. Alternately, if the pressure is half, the volume of gas is doubled.

**Charles’s Law**

V Î± T

V_{1}/T_{1} = V_{2}/T_{2 }or V_{2}/V_{1} =T_{2}/T_{1 }or V_{1}T_{2} = V_{2}T_{1. }

Charles’s Law is also known as the law of **volumes** and designates that gases expand when heated. The gas volume is directly proportional to the absolute temperature (Kelvin scale) if a gas’s pressure remains constant. If the absolute temperature (T) of a gas doubles, the volume is doubled, and vice versa.

**Gay-Lussac’s Law**

P_{i}/T_{i} = P_{f}/T_{f}

Gay Lussac’s Law (ideal gas law) states that a gas’s pressure is proportional to the absolute temperature. In other words, if we double the pressure of a gas, the absolute temperature will double, and vice versa.

P_{i} = initial pressure

T_{i} = initial absolute temperature

P_{f} = final pressure

T_{f} = final absolute temperature

**Avogadro’s Law**

V Î± n

V_{1}/n_{1} = V_{2}/n_{2}

Avogadro’s Law suggests that for a given mass of an **ideal gas,** the volume and amount of gas (n – moles) are proportional if the temperature and the pressure are constant. As the moles (n) increase, the volume also increases proportionately.

**Combined Gas Law**

pV/T = k

When we combine Boyle’s Law, Charles’s Law, and Gay-Lussac’s law, a single expression called the Combined Gas Law equation results. This law states that the ratio between the pressure volume and the system’s temperature remains constant (k) and expresses as units of energy divided by temperature.

**Ideal Gas Law**

Based on kinetic principles, gas molecules colliding with the walls containing them creates gas molecules’ pressure. The more molecules (per unit volume) generate more collisions, which raises the pressure. The kinetic energy of gas molecules is generally proportional to the temperature (absolute). While the molecules are at rest, at absolute zero, the molecules increase in speed at high temperatures, and pressure rises. When combining these concepts, we have the Ideal Gas equation.

PV = nRT

The Ideal Gas Law is similar to the Combined Gas Law. The law is an equation of an **ideal gas **(R) state and conforms to Boyle’s, Charles’s, and Avogadro’s Laws. It is hypothetical and estimates the behavior of gases based on specific conditions. It suggests that the volume (V), pressure (P), and temperature (T) determine the state and amount (n) of a gas.

We demonstrate how simple variables, such as temperature and pressure influence gas measurement and impact gas instrumentation when reviewing these gas laws. For this reason, metering applications require temperature and pressure compensation to ensure accurate measurement and minimize waste.