The Gas Laws

During high pressure or high-temperature circumstances, a tyre inflated with air is at the risk of exploding. Or when ascending a mountain you start noticing troubles to inhale.  With changing physical conditions the action of gaseous particles also differs from their regular nature. The behaviour of a Gas may be analysed by several laws known as the Gas laws.

All gases typically display similar behaviours when the circumstances are normal. But with a minor change in physical variables like pressure, temperature or volume they reveal a divergence. Gas laws are a study of this behaviour of gases. The variables of state like the Pressure, Volume and Temperature of a gas indicate its real nature. Therefore gas laws are connections between these variables.

Charles’s Law

Jacques Charles in 1787 investigated the influence of temperature on the volume of a gaseous material at a constant pressure. He completed this investigation to understand the technology underlying the hot air balloon flying. According to his conclusions, for constant pressure and for constant mass, the volume of a gas is precisely proportional to the temperature.

This indicates that with the rise in temperature the volume must grow while with lowering temperature the volume falls. In his experiment, he determined that the increase in volume with every degree equaled 1/273.15 times of the initial volume. Thus, if the volume is V0 at 0° C & Vt is the volume at t° C then,

Vt = V0 +t/273.15 V0 ⇒ Vt = V0 (1+ t/273.15 )

⇒ Vt = V0 (273.15+ t/273.15 )

For the purpose of measuring the measurements of gaseous stuff at temperature 273.15 K, we utilize a particular scale called the Kelvin Temperature Scale. The measurements of temperature (T) on this scale is 273.15 more than the temperature (t) of the conventional scale.

T= 273.15+t

Whereas, when T = 0° c then the value on the Celsius scale is 273.15. The Kelvin scale is sometimes termed Absolute Temperature Scale or Thermodynamic Scale. This scale is employed in all scientific tests and operations. In the equation [ Vt = V0 (273.15+ t/273.15 ) ] if we pick the numbers Tt = 273.15+t and T0 = 273.15 then:

Vt = V0 ( Tt / T0 )

This implies Vt/V0= (Tt / T0 ), which may alternatively be expressed as:

V2/V1= T2/ T1

or V1 /T1 = V2 / T2

V/T = constant = k2

Therefore, V= k2 T

Charles’s Law has the following issues:

According to Charles’s Law, volume immediately rises or decreases as volume grows or decreases. Since the volume reduces proportionately with the temperature, it follows that the temperature drops. According to theory, the gas volume should fall until it hits zero as the temperature declines. As a result, it would seem that gas should have no volume at absolute zero (a theoretical temperature where gas has zero energy and hence can’t move).  it is true that Charles and Gay-Lussac didn’t have experience with liquid air at the period of their study, since liquid air wasn’t developed until 1877 even though Charles thought gases such as hydrogen and oxygen could be liquefied.

Boyle’s law

In 1662 Robert Boyle explored the link between volume and pressure of a gas of fixed quantity at constant temperature. He noticed that volume of a given mass of a gas is inversely related to its pressure at a fixed temperature. Boyle’s law, published in 1662, asserts that, at constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. It may be proven experimentally using a pressure gauge and a variable volume container. It may also be derived from the kinetic theory of gases: if a container, with a certain number of molecules within, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, generating a larger pressure

Combined Gas Law

The combined gas law includes the 3 gas laws given by Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law.  It asserts that the ratio between the product of pressure and volume and the absolute temperature of a gas is equal to a constant. When Avogadro’s law is applied to the combined gas law, the ideal gas law results. Unlike the named gas laws, the combined gas law doesn’t have an acknowledged discoverer. It is just a mixture of the other gas laws that works when everything but temperature, pressure, and volume are maintained constant.

There are a handful of typical formulae for formulating the combined gas law. The classic law links Boyle’s law and Charles’ law to state

PV/T = k

Where P = pressure, V = volume, T = absolute temperature (Kelvin), and k = constant.

The constant k is a genuine constant if the quantity of moles of the gas doesn’t vary. Otherwise, it varies.

Another typical formula for the combined gas law links “before and after” circumstances of a gas:

P1V₁ / T1 = P2V2 / T2

The combined gas law has practical uses when working with gases at typical temperatures and pressures. Like other gas laws based on ideal behaviour, it becomes less accurate at high temperatures and pressures. The law is utilized in thermodynamics and fluid mechanics. For example, it may be used to compute pressure, volume, or temperature for the gas in clouds to forecast weather.

Conclusion:

Laws that connect the pressure, volume, and temperature of a gas are gas laws. Boyle’s law, named after Robert Boyle, states that, at constant temperature, the pressure P of a gas changes inversely with its volume V, or PV = k, where k is a constant. Charles’s law named for J.-A.-C. Charles states that, under constant pressure, the volume V of a gas is precisely proportional to its absolute (Kelvin) temperature T, or V/T = k. These two equations may be combined to make the ideal gas law, a single description of the behaviour of gases known as an equation of state, PV = nRT, where n is the number of gram-moles of a gas and R is termed as the universal gas constant. Though this rule explains the conduct of an ideal gas, it roughly approximates the behaviour of actual gases.