Kinetic Theory | Class 11 Physics Notes

12.3 Behaviour of gases

This section discusses the macroscopic behavior of gases and their relation to molecular properties. Gases are easier to understand than solids and liquids because their molecules are far apart, making intermolecular interactions negligible except during collisions. At low pressures and high temperatures (well above liquefaction points), gases approximately obey the relation P V = K T, where P is pressure, V volume, T absolute temperature, and K a constant for the sample. Introducing the molecular concept, K is proportional to the number of molecules N, so K = N k_B, where k_B is Boltzmann's constant, universal for all gases. This leads to the relation (P V)/(N T) = k_B, consistent with Avogadro's hypothesis that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. The number of molecules in 22.4 liters of any gas at standard temperature and pressure (STP) is Avogadro's number, N_A = 6.02 × 10^23. The mass of 22.4 liters of a gas equals its molecular weight in grams at STP, defining a mole. The ideal gas equation is written as P V = μ R T, where μ is the number of moles and R = N_A k_B is the universal gas constant (8.314 J mol^-1 K^-1). The equation can also be expressed as P V = k_B N T or P = k_B n T, where n is number density. Another useful form relates pressure to mass density ρ as P = (ρ R T)/M_0, where M_0 is molar mass. Real gases deviate from ideal behavior at high pressures and low temperatures but approach ideal gas behavior at low pressures and high temperatures, as shown in Fig. 12.1. Fixing μ and T, Boyle's law (P V = constant) is recovered; fixing P, Charles' law (V ∝ T) is observed. Dalton's law of partial pressures states that the total pressure of a gas mixture is the sum of partial pressures of individual gases, each behaving ideally. Several examples illustrate molecular volume, molecular size, interatomic distances, and partial pressure calculations. These concepts connect molecular properties to measurable macroscopic gas behavior.

📊 Diagram: Fig.12.1 Real gases approach ideal gas behaviour at low pressures and high temperatures.; Fig. 12.2 Experimental P-V curves (solid lines) for steam at three temperatures compared with Boyle's law (dotted lines). P is in units of 22 atm and V in units of 0.09 litres.; Fig. 12.3 Experimental T-V curves (solid lines) for CO2 at three pressures compared with Charles' law (dotted lines). T is in units of 300 K and V in units of 0.13 litres.

🔗 Connection: This section's understanding of gas behavior leads to the molecular kinetic theory model of an ideal gas, which is developed in the next section.