KINETIC THEORY
Frequently Asked Questions
It is a theory that explains the macroscopic properties of gases (pressure, temperature, volume) in terms of the microscopic motion of gas molecules.
Gas consists of a large number of molecules in random motion; intermolecular forces are negligible except during collisions; collisions are elastic; molecular size is negligible compared to separation.
An ideal gas is a hypothetical gas that obeys the equation \(PV = nRT\) exactly at all pressures and temperatures.
Because real gases have finite molecular size and intermolecular forces, which cause deviations at high pressure and low temperature.
\(PV = nRT\), where \(P\) is pressure, \(V\) volume, \(n)\ number of moles, \(R)\ gas constant, and \(T\) absolute temperature.
\(R = 8.314, \text{J mol}^{-1}\text{K}^{-1}\).
It is the constant that relates temperature to energy at the molecular level: \(k_B = 1.38 \times 10^{-23},\text{J K}^{-1}\).
Pressure arises due to momentum transfer when gas molecules collide elastically with the walls of the container.
\(P = \frac{1}{3}\frac{Nm}{V}\overline{c^2}\).
Temperature is a measure of the average translational kinetic energy of gas molecules.
\(\overline{E_k} = \frac{3}{2}k_B T\).
No, it depends only on temperature.
It is defined as \(c_{\text{rms}} = \sqrt{\overline{c^2}} = \sqrt{\frac{3RT}{M}}\).
It is the speed possessed by the maximum number of molecules at a given temperature.
It is the average speed of all molecules in a gas.
\(c_{\text{rms}} > c_{\text{mean}} > c_{\text{mp}}\).
It is the total kinetic energy of all molecules and depends only on temperature.
\(U = \frac{3}{2}RT\).
It states that energy is equally distributed among all active degrees of freedom, each contributing \(\frac{1}{2}k_BT\).
It is an independent way in which a molecule can store energy.
Three (only translational).
Five (3 translational + 2 rotational).
Five at ordinary temperature (NCERT standard).
It is the heat required to raise the temperature of one mole of gas by 1 K at constant volume.
\(C_P - C_V = R\) for all ideal gases.
\(\gamma = \frac{5}{3}\).
\(\gamma = \frac{7}{5}\).
It is the average distance travelled by a molecule between two successive collisions.
\(\lambda = \frac{1}{\sqrt{2}\pi d^2 n}\).
Mean free path decreases as pressure increases.
Due to frequent molecular collisions that continuously change direction.
Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules.
\(N_A = 6.02 \times 10^{23},\text{mol}^{-1}\).
The total pressure of a mixture of gases equals the sum of their partial pressures.
It is the pressure a gas would exert if it alone occupied the given volume at the same temperature.
At low pressure and high temperature.
Absolute temperature is directly proportional to molecular kinetic energy.
Because quantum effects become significant and equipartition law breaks down.
Processes like diffusion, viscosity, and thermal conductivity explained using kinetic theory.
Derivations, numerical problems, conceptual MCQs, degrees of freedom, specific heats, and mean free path.
Because gas molecules continuously collide with each other and the container walls, causing constant and unpredictable changes in direction and speed.
Elastic collisions ensure conservation of kinetic energy, allowing temperature to remain well-defined and constant in equilibrium.
Because the actual volume of molecules is extremely small compared to the volume occupied by the gas under ordinary conditions.
The rms speed increases by a factor of \(\sqrt{2}\), since \(c_{\text{rms}} \propto \sqrt{T}\).
Because there are no intermolecular forces, so internal energy consists only of kinetic energy of molecules.
Decreasing volume increases collision frequency with container walls, increasing pressure such that \(PV\) remains constant at constant temperature.
It is the number of molecules per unit volume, given by \(n = \frac{N}{V}\).
At low temperatures, some degrees of freedom become inactive due to quantum effects.
It explains viscosity as the result of momentum transfer between layers of gas molecules moving at different speeds.
It connects microscopic physics with macroscopic laws, includes derivations, numericals, and conceptual questions frequently asked in board and competitive exams.
