This chapter explains the kinetic theory of gases, detailing how gas behaves due to the movement of its molecules. Understanding this theory is fundamental for grasping the properties of gases and their interactions.
Kinetic Theory – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the Kinetic Theory chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
PV = nRT
P is pressure (Pa), V is volume (m³), n is the number of moles, R is the universal gas constant (8.314 J/(mol·K)), and T is the absolute temperature (K). This equation represents the ideal gas law, which relates the state of an ideal gas.
PV = NkT
P is pressure, V is volume, N is the number of molecules, k is the Boltzmann constant (1.38 × 10⁻²³ J/K), and T is temperature. This formulation of the ideal gas law uses molecular quantities.
E = (3/2)NkT
E is the total translational kinetic energy of the gas, N is the number of molecules, k is Boltzmann's constant, and T is temperature. This shows the dependency of average kinetic energy on temperature.
P = (1/3)nmu²
P is pressure, n is number density (molecules per unit volume), m is mass of a molecule, and u is the average speed of molecules. This relates kinetic pressure to molecular motion.
l = (kT)/(√2πd²Pn)
l is the mean free path, T is absolute temperature, d is the diameter of the molecule, P is pressure, and n is number density. It indicates the average distance a molecule travels between collisions.
C_v = (3/2)R
C_v is the molar specific heat at constant volume, and R is the universal gas constant. For monatomic gases, this expresses the basic heat capacity relation.
C_p = C_v + R
C_p is the molar specific heat at constant pressure. This relation connects the specific heats at constant volume and pressure, emphasizing their difference by the gas constant.
U = (3/2)nRT
U is the total internal energy for one mole of a monatomic ideal gas, showing its dependence on temperature and the number of moles.
v_rms = √(3RT/M)
v_rms is the root mean square speed, R is the universal gas constant, T is the absolute temperature, and M is the molar mass. This gives the speed of molecules based on temperature and mass.
P_total = P_1 + P_2 + ...
P_total is the total pressure exerted by a mixture of non-reactive gases, with each P being the partial pressure of a different gas. Represents Dalton's Law of Partial Pressures.
Equations
PV = NkT
This equation connects pressure, volume, number of molecules, and temperature for an ideal gas.
P = nRT/V
Rearrangement of the ideal gas law to express pressure in terms of number density, temperature, and volume.
E = (3/2)NkT
Internal energy of a monatomic ideal gas, reflecting the dependence on temperature.
P = (1/3)nmu²
Derivation for pressure in terms of number density and average kinetic energy of molecules.
l = kT / (√2πd²n)
Mean free path based on temperature and molecular interaction.
C_v = (3/2)R
Specific heat capacity for monatomic gases at constant volume.
C_p = C_v + R
Relationship between specific heats at constant volume and pressure.
U = (3/2)nRT
Total internal energy for a mole of monatomic ideal gas.
v_rms = √(3RT/M)
Root mean square speed as a function of temperature and molar mass.
P_total = P_1 + P_2 + ...
Dalton's law stating that total pressure is the sum of the partial pressures of individual gases in a mixture.
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