About Perfect Gas
In the entire universe, there is no such gas that possesses the properties of a perfect gas. An ideal gas law states the relationship between the pressure applied by a gas, the amount of gaseous substance, the absolute temperature of the gas, and the volume occupied by the gas. A gas that perfectly obeys the law of ideal gas is known as a perfect gas or general gas law.
The ideal gas law, despite its limitations, is a good approximation of the behavior of many gasses in several conditions. The ideal gas law, developed by Benoit Paul Émile Clapeyron in 1834 stated that it's a combination of the below laws:
Empirical Charles's law
Boyle's law
Avogadro's law
Gay Lussac's law
In short, the ideal gas law states that the product of one gram molecule's pressure and volume is equal to the product of the gas's absolute temperature and the universal gas constant.
Equation: PV=nRT
where,
P is the pressure
V is the volume
n is the amount of substance
R is the ideal gas constant
Ideal Gas Equation Units
When using the gas constant R = 8.31 J/K.mol, we must enter the pressure P in pascals Pa, volume in m3, and temperature T in kelvin K.
When using the gas constant R = 0.082 L.atm/K.mol, pressure should be measured in atmospheres atm, volume measured in litres L, and temperature measured in Kelvin K.
The ideal gas law is based on Robert Boyle's, Gay- Lussac's, and Amedeo Avogadro's observations. We arrive at the Ideal gas equation, which describes all of the relationships simultaneously, by combining their observations into a single formula.
The following are the three distinct expressions:
Boyle’s Law
V ∝ 1/P
Charle’s Law
V ∝ T
Avagadro’s Law
V ∝ n
When these 3 are combined it gives:
V ∝ nT/P
Volume is proportional to the number of moles and temperature, but inversely proportional to pressure, as shown by the equation above.
The following is a rewrite of this expression:
V = RnT/P = nRT/P
To get clear of the fraction, multiply both sides of the equation by P.
PV = nRT
The ideal gas equation is depicted in the above equation.
Perfect Gas Law
The general perfect gas law is derived from the kinetic theory of gases. Its assumptions state that
The volume of molecules is very small as compared to the volume that has been occupied by the gas
The gas contains many molecules that move in random motion and obey Newton's law of motion.
Except during the elastic collision, there are no forces that act on the molecules.
No gas has only these properties. The behavior of the real gasses is closely studied by the perfect gas law at a very high temperature and low pressure when a maximum distance between the molecules and their high speeds moves ahead of this interaction. Gas will not obey the equation when the situation is such that the gas gets liquefied near its condensation point.
Types of a Perfect Gas
A perfect gas is simplified into two to more general perfect gases which are as follows:
1. Calorically Perfect Gas
Calorically perfect gas is the most restricted gas model that still gives accurate and reasonable calculations. For instance, if a compression stage of one model of the axial compressor is made having a variable, Cp and constant, Cv to compare the simplifications, then the derivation is found at a small order of magnitude. This gives a major impact on the final result Cp.
The expression of a calorically perfect gas is generalized as follows:
e = CvTh = CpT
2. Thermally Perfect Gas
Thermally perfect gas is present in thermodynamics equilibrium. It does not react chemically. The functions of temperature are only applied in this case that are enthalpy, specific heat, and internal energy. This type of gas is generally used for modelling. For instance, if an axial compressor with limited temperature for fluctuations does not cause any significant deviations, then the heat capacity is still liable to vary only through temperature and the molecules are not allowed to disassociate.
e = e(T)h = h(T)de = CvdTdh = CpdT
FAQs on Perfect Gas
1. What is a perfect gas and what is its governing equation?
A perfect gas is a theoretical gas composed of particles that move randomly and do not interact with each other. It perfectly obeys the general gas laws under all conditions of temperature and pressure. The behaviour of a perfect gas is described by the Perfect Gas Equation (also known as the Ideal Gas Law):
PV = nRT
Where:
- P is the pressure of the gas.
- V is the volume it occupies.
- n is the number of moles of the gas.
- R is the universal gas constant.
- T is the absolute temperature of the gas in Kelvin.
2. What are the key assumptions a gas must satisfy to be considered a perfect gas?
For a gas to be considered a perfect gas, it must adhere to the assumptions of the Kinetic Theory of Gases. The main assumptions are:
- The volume of the gas molecules is negligible compared to the total volume occupied by the gas.
- There are no intermolecular forces of attraction or repulsion between the gas molecules.
- The gas consists of a large number of molecules in constant, random motion, obeying Newton's laws.
- Collisions between molecules, and between molecules and the container walls, are perfectly elastic, meaning no kinetic energy is lost.
3. What is the main difference between a perfect gas and a real gas?
The main difference lies in the assumptions made. A perfect gas is a theoretical concept where intermolecular forces and the volume of gas molecules are considered zero. In contrast, a real gas, which is any gas that actually exists (like oxygen, nitrogen, etc.), has finite molecular volume and experiences weak intermolecular forces. Real gases deviate from perfect gas behaviour, especially at high pressures and low temperatures, where molecules are closer together.
4. Under what conditions can a real gas, like nitrogen or oxygen, behave like a perfect gas?
A real gas behaves most like a perfect gas under conditions of high temperature and low pressure. This is because:
- At high temperatures, the kinetic energy of the molecules is very high, which easily overcomes the weak intermolecular forces of attraction.
- At low pressures, the gas expands to fill a large volume, making the volume of the individual molecules negligible in comparison to the total volume.
Under these conditions, the two main assumptions of a perfect gas become reasonably valid for a real gas.
5. How are Boyle's Law, Charles's Law, and Avogadro's Law combined to derive the Perfect Gas Equation?
The Perfect Gas Equation is a synthesis of three fundamental gas laws:
- Boyle's Law states that volume is inversely proportional to pressure (V ∝ 1/P) at constant temperature and moles.
- Charles's Law states that volume is directly proportional to absolute temperature (V ∝ T) at constant pressure and moles.
- Avogadro's Law states that volume is directly proportional to the number of moles (V ∝ n) at constant temperature and pressure.
By combining these proportionalities, we get V ∝ nT/P. To turn this into an equation, we introduce a proportionality constant, R (the universal gas constant), giving V = R(nT/P), which rearranges to the familiar form PV = nRT.
6. Why is the concept of a perfect gas useful in Chemistry if no such gas truly exists?
The concept of a perfect gas is extremely useful as a simplified model that provides a very good approximation of the behaviour of most real gases under common conditions. It serves as a fundamental baseline for understanding the physical properties of gases and their relationships between pressure, volume, temperature, and amount. For calculations in stoichiometry and thermodynamics under standard conditions, the Perfect Gas Equation offers accurate results without the complexity of equations for real gases, like the van der Waals equation.
7. How do 'thermally perfect gas' and 'calorically perfect gas' differ in thermodynamics?
Both are simplifications of the perfect gas model used in thermodynamics, differing in their assumptions about heat capacity:
- A thermally perfect gas is a perfect gas where the specific heats (Cp and Cv) are assumed to be a function of temperature only. This is a good approximation for many gases over a moderate temperature range where there is no chemical reaction or dissociation.
- A calorically perfect gas is a more restrictive model. It is a thermally perfect gas where the specific heats (Cp and Cv) are assumed to be constant, regardless of temperature. This simplification is often used in introductory calculations where temperature changes are not extreme.
In short, all calorically perfect gases are thermally perfect, but not all thermally perfect gases are calorically perfect.
