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Temperature is a measurement of how hot or cold a body is. It is a measurement of the average kinetic energy of the particles in an object, which is a sort of energy related to motion.
Theoretically, an ideal gas exists. It does not exist in reality, but it is imagined to exist to make calculations easier. It also serves as a benchmark against which other gases’ behaviour can be compared.
Temperature and Ideal Gas Equation
Temperature
Temperature is the attribute of a substance which determines the quantity of heat present in it. Temperature represents the degree of hotness or coldness of a body as a function of its average kinetic energy.
Kelvin is the standard unit (or SI unit) of the temperature.
Temperature is measured on a various scale, but the most common are Fahrenheit, Celsius, and Kelvin.
Ideal Gas
An ideal gas is defined as a gas made up of randomly moving particles, much like all other gases. The only difference is that when the particles of an ideal gas meet, the collisions are considered to be perfectly elastic, meaning that none of the particles’ energy is wasted.
When actual gas particles contact, however, some of their energy is lost in the process of changing directions and overcoming friction. Most natural gases, however, behave exactly like an ideal gas when exposed to acceptable limitations at STP.
Ideal Gas Equation
The ideal gas equation is the equation that describes the simultaneous influence of pressure and temperature on the volume of a gas. It’s sometimes referred to as the combined gas law. The ideal gas equation is also described as the equation that shows how pressure and temperature affect the volume of a gas at the same time.
Ideal gas equation is given as
PV = nRT
Derivation of Ideal Gas Equation
Ideal gas equation can be derived by using three laws which are given here.
Boyle’s Law
Charles’ Law
Avagadro’s Law
Boyle’s Law
Robert Boyle studied the changes in volume of a gas by adjusting the pressure of a certain amount of gas at a constant temperature. He collected some air in the tube’s tip and calculated the pressure exerted by the gas using the difference in mercury height between the tube’s two arms. By adding more mercury to the tube, the pressure of the gas is increased while the volume of the gas is reduced.
“The absolute pressure which is exerted by a given mass of an ideal gas is inversely proportional to the volume occupied by the gas if both the temperature and the amount of gas stay unchanged”. This is the statement of Boyle’s Law.
Boyle’s law is given as
P∝1V ———– (1)
And
P=K 1/V
PV=K
P = pressure
V = volume
K = constant
Charles’ Law
In 1787 Jacques Charles examined the effect or influence of temperature on volume of a gaseous substance at constant pressure. He performed this analysis in order to know the fact behind hot air balloon flight. According to his analysis, the volume of a gas is directly proportional to the temperature at constant pressure and mass.
It means that when the temperature rises, the volume also rises and when the temperature decreases, then also the volume decreases.
When the pressure of a sample of air is held constant, the volume of the gas is precisely proportional to its temperature. This the statement of Charles’ law.
Charles’ law is given as
V∝T ———- (2)
V = CT
Here, C = constant
Avagadro’s Law
Amedeo Avogadro combined Dalton’s atomic theory and Gay Lussac’s law in 1811 to derive Avogadro’s law, another significant gas law. According to Avogadro’s law, at constant temperature and pressure, all gases contain an identical number of molecules. Simply put, the volume of a gas is directly proportional to the number of molecules present in that gas under constant temperature and pressure.
Avagadro’s law is given as
V∝n ———- (3)
Here,
n = number of moles
Therefore, from equations (1), (2), and (3), we get the ideal gas equation.
From equations (1), (2), and (3), we get
V∝1/P×T×n
V=R 1/P×T×n
Therefore, the ideal gas equation is
PV=nRT
Here,
P = pressure
V = volume
T = temperature
R = gas constant
n = number of moles
Absolute Temperature
Absolute temperature is also known as thermodynamic temperature. At this temperature, a system’s thermodynamic energy is lowest. Absolute temperature which is equals to zero or -273 degree Celsius, often known as absolute zero, is equivalent. At absolute zero temperature, the gas particles’ motion comes to a halt. This means that the gas particles aren’t actually moving. The volume of a gas is zero at absolute zero. As a result, a gas’s volume is determined by its absolute zero.
Conclusion
Temperature represents the degree of hotness or coldness of a body as a function of its average kinetic energy.
Kelvin is the standard unit (or SI unit) of the temperature.
An ideal gas is defined as a gas made up of randomly moving particles, much like all other gases.
Ideal gas equation is given as
PV = nRT
Ideal gas equation can be derived by using three laws which are given here.
Boyle’s Law
Charles’ Law
Avagadro’s Law
Boyle’s law is given as
P∝1/V
Charles’ law is given as
V∝T
Avagadro’s law is given as
V∝n
The ideal gas equation is
PV=nRT
