Q.One mole of an ideal gas at 300 K is contained in a cubical vessel of volume V whose eight corners are labelled A, B, C, D, E, F, G, H, so that ABCD and EFGH are two opposite (parallel) faces of the cube. The face EFGH is made of a material that totally absorbs every gas molecule that strikes it (the molecules are not reflected back), while the opposite face ABCD reflects molecules in the usual way. At any given instant, which statement about the pressure on the faces is correct?
Concept understanding — Kinetic Theory Explanation
Kinetic Theory Explanation
Imagine you're sitting in a quiet room. The air around you feels still, but it isn't. Every second, billions of tiny particles — molecules of nitrogen and oxygen — are zipping past you at hundreds of metres per second. You don't feel them because they're too small, and they're moving in every direction at once. But if you put your hand near a hot stove, you suddenly feel heat. Why?
The answer is the kinetic theory of matter. It's a way of explaining what we observe at the human scale (temperature, pressure, heat) by thinking about what's happening at the molecular scale.
The core idea
The kinetic theory says three simple things:
- All matter is made of tiny particles (atoms or molecules) that are in constant, random motion.
- The particles collide with each other and with the walls of their container — these collisions are perfectly elastic (no energy is lost).
- The average kinetic energy of these particles is directly proportional to the temperature of the substance.
That's it. Everything else — pressure, diffusion, the way a gas expands when heated — follows from these three statements.
Building intuition
Think of a single gas molecule bouncing around inside a box. It hits a wall, bounces off, and keeps going. Each time it hits the wall, it exerts a tiny force. Now multiply that by billions of molecules hitting every square centimetre of wall every second. That constant, collective force is what we measure as pressure.
Now heat the box. The molecules move faster — their average kinetic energy increases. They hit the walls harder and more often. Pressure goes up. If the walls can move (like a piston), the gas expands until the pressure inside equals the pressure outside.
This is why a bicycle tyre feels hot after you pump it: you're doing work on the air, compressing it, which increases the average kinetic energy of the molecules — and that's exactly what temperature is.
Temperature is not the total kinetic energy of all molecules — it's the average kinetic energy per molecule. A large cold object can have more total energy than a small hot one, but its molecules move slower on average.
The precise statement
For an ideal gas (a gas where intermolecular forces are negligible and collisions are perfectly elastic), the kinetic theory gives us a direct mathematical link:
Average kinetic energy per molecule=23kBT
where kB is Boltzmann's constant (1.38×10−23J/K) and T is the absolute temperature in Kelvin.
This means that at the same temperature, all gas molecules — regardless of their mass — have the same average kinetic energy. A light hydrogen molecule moves faster than a heavy oxygen molecule at the same temperature, but their average kinetic energies are equal.
From this, we can derive the ideal gas law:
PV=31Nmv2=NkBT
where P is pressure, V is volume, N is the number of molecules, m is the mass of one molecule, and v2 is the mean square speed.
PV=nRT
This is the familiar ideal gas law. The kinetic theory shows it's not just an empirical rule — it follows directly from the motion of molecules.
What the theory explains
The kinetic theory isn't just abstract. It explains everyday phenomena:
- Evaporation cools you: The fastest molecules escape from a liquid surface, leaving behind slower ones. The average kinetic energy drops — so the temperature drops.
- Diffusion: Molecules spread out because they're constantly moving and colliding, gradually mixing with neighbouring molecules.
- Brownian motion: Pollen grains jitter under a microscope because they're being bombarded unevenly by invisible water molecules.
- Why gases are compressible but liquids aren't: In a gas, molecules are far apart with lots of empty space. In a liquid, they're already touching.
A common mistake is to think that all molecules in a gas move at the same speed. They don't — there's a distribution of speeds (the Maxwell-Boltzmann distribution). Some are slow, some are very fast, but most are near the average. Temperature changes the shape of this distribution, not just the average.
The limits
The kinetic theory as described works perfectly for ideal gases. Real gases deviate at high pressures (molecules get close enough for forces to matter) and low temperatures (molecules slow down enough for attractions to become significant). But even then, the theory gives us a starting point — we add corrections (like van der Waals equation) to account for real behaviour.
For solids and liquids, the same basic idea applies — particles vibrate about fixed positions (solids) or slide past each other (liquids) — but the mathematics becomes more complex because the particles are never far apart.
The takeaway
The kinetic theory is a bridge between the microscopic world we can't see and the macroscopic world we experience. It tells us that heat is motion, pressure is collisions, and temperature is average energy. Once you internalise that, a huge chunk of physics and chemistry becomes intuitive.
Many students find this page while searching "Kinetic Theory Explanation formula physics" or "Kinetic Theory Explanation important questions and answers"; the concept sits firmly within the Class 11 Physics NCERT/CBSE syllabus. It's also a frequent building block for numericals in JEE Main, NEET and state engineering/medical entrance exams, so treating it as a one-time memorisation task rather than an understood idea tends to backfire later.
Pressure is the rate at which molecules hand momentum to a wall. A reflecting wall (ABCD) gets 2mv per hit; the absorbing wall EFGH gets only mv per hit because the molecule sticks instead of bouncing back. So EFGH feels half the pressure of ABCD.
On ABCD each molecule reverses, changing momentum by 2mv; on EFGH it is captured, changing momentum by mv. With the same flux of molecules striking both faces, the pressure is proportional to the momentum delivered per hit, so pEFGH=21pABCD.
(D) The pressure on EFGH would be half that on ABCD.
The pressure on a wall equals the rate at which molecules deliver momentum to it. An ordinary reflecting wall receives 2mv from each normal hit, but the absorbing face EFGH receives only mv per hit (the molecule is captured, it does not rebound). Hence EFGH experiences half the pressure of the opposite reflecting face ABCD.
Concept
Gas pressure is the average force per unit area that molecules exert on a wall, and this force is the rate of momentum transfer per unit area during collisions.
Why this formula
For a molecule whose velocity component normal to the wall has magnitude v:
- Striking a normal (reflecting) wall it bounces straight back, so its momentum changes by
Δpreflect=mv−(−mv)=2mv.
- Striking the absorbing face EFGH it sticks and does not return, so
Δpabsorb=mv−0=mv.
Steps
- At any instant the same flux of molecules (same number density and speed distribution) strikes both opposite faces.
- Each strike on ABCD transfers 2mv; each strike on EFGH transfers mv.
- Pressure is proportional to the momentum delivered per collision, so
pEFGH=21pABCD.
Why the distractors fail
- (A) is wrong: absorbed molecules still deliver momentum mv, so the pressure is not zero.
- (B) is wrong: a reflecting face and an absorbing face cannot feel the same pressure.
- (C) is wrong: absorption halves, not doubles, the momentum transfer.
(D) The pressure on EFGH would be half that on ABCD.
Quick way to see it: think in terms of momentum 'kicks,' not a full flux integral. A reflecting wall gives each molecule a full bounce-back — it reverses the molecule's momentum, delivering 2mv to the wall. An absorbing wall is like a perfectly inelastic catch: the molecule's momentum is transferred once and never returned, delivering only mv. Since the same stream of molecules hits both parallel faces per unit time, the absorbing face simply gets 'half the kick' per collision compared to the reflecting face, so pEFGH=21pABCD — no need to track the full collision-rate calculation to see why the factor is exactly 2.
- AP EAPCET 2022Set ap-2022-07-12-FN1 markMCQQ.Principles of molecular interactions and thermal energy can be used to explain (I) Vapour Pressure (II) Surface Tension (III) Viscosity (A) (I) and (II) only (B) (II) and (III) only (C) (I) and (III) only (D) (I), (II) and (III)
›Reveal solutionSolution
All three phenomena — vapour pressure, surface tension, and viscosity — arise from the competition between intermolecular attractive forces and the thermal kinetic energy of molecules. Answer: all three, (D).
Concept and Intuition
Molecules in a liquid are held together by intermolecular attractive forces, but they also possess thermal kinetic energy that lets them move and, at the surface, occasionally escape. Vapour pressure is set by how many molecules have enough thermal energy to overcome the attractive pull and evaporate. Surface tension arises because surface molecules feel a net inward pull from their neighbours (fewer neighbours above), an effect governed by the strength of intermolecular forces relative to thermal jostling. Viscosity reflects the internal friction between layers of a fluid sliding past each other, which again depends on how strongly molecules interact and how much thermal energy resists that ordered interaction.
Step-by-Step Solution
- Vapour pressure: molecules escape the liquid surface once their thermal KE exceeds the attractive potential holding them in — directly a molecular-interaction/thermal-energy balance.
- Surface tension: surface molecules experience net inward intermolecular attraction (asymmetric neighbour distribution), which is why it depends on both the interaction strength and temperature (thermal agitation reduces it).
- Viscosity: internal resistance to flow depends on intermolecular cohesion resisting relative motion between fluid layers, and thermal energy that allows molecules to move past one another.
- All three are explainable through the same underlying framework, so the correct choice includes all of them.
Common Mistakes
- Assuming surface tension and viscosity are purely "mechanical" properties unrelated to thermal energy — temperature dependence of both confirms the thermal-energy link.
- Excluding viscosity, forgetting that liquid viscosity actually decreases with temperature precisely because of this molecular-interaction/thermal-energy competition.
✓Final answerThe correct option is (D) — (I), (II) and (III).
ANSWER: D
- AP EAPCET 2022Set eng-2022-07-06-AN1 markMCQQ.Assertion (A) : When an ideal gas is compressed adiabatically its temperature and the average kinetic energy of the gas molecules increase. Reason (R) : The kinetic energy increases because of collisions of molecules with moving parts of wall only. (A) (A) and (R) are true and (R) is correct explanation of (A) (B) (A) and (R) are true but (R) is not correct explanation of (A) (C) (A) is true and (R) is false (D) (A) is false and (R) is true
›Reveal solutionSolution
Both statements are true, and the moving-wall-collision mechanism in the Reason is indeed the correct microscopic explanation for why adiabatic compression raises the gas's temperature.
Concept and Intuition
Thermodynamically, adiabatic compression means Q=0, so all the work done ON the gas goes into raising its internal energy (and hence temperature, for an ideal gas). Kinetic theory gives the microscopic picture: a gas molecule that elastically collides with a wall moving toward it (as the piston advances) rebounds with a higher speed than it had — exactly like a ball gaining speed when struck by an approaching bat/paddle. Collisions with a stationary wall, by contrast, are perfectly elastic in the sense that the molecule's speed (in the wall's frame) doesn't change. So it is precisely the collisions with the moving piston that pump kinetic energy into the gas.
Step-by-Step Solution
- Assertion: during adiabatic compression, Q=0 and work is done on the gas, so ΔU=−Wbygas>0 (since Wbygas<0 for compression). For an ideal gas, U∝T, so T rises, and since average KE per molecule ∝T, the average KE also rises. Assertion is true.
- Reason: microscopically, gas molecules colliding with the moving piston gain kinetic energy (like a ball bouncing off a moving bat), while collisions with the fixed side walls leave a molecule's kinetic energy unchanged. So the increase in average KE genuinely originates only from moving-wall (piston) collisions. Reason is true.
- Since the Reason correctly identifies the true microscopic mechanism behind the Assertion, it is the correct explanation.
Common Mistakes
- Dismissing the Reason as false because of the word "only," without recognizing that it is in fact the accurate description of the microscopic mechanism (stationary-wall collisions don't change KE).
- Confusing this with isothermal compression, where temperature would stay constant.
✓Final answerThe correct option is (A) — (A) and (R) are true and (R) is the correct explanation of (A).
ANSWER: A
- AP EAPCET 2021Set ap-2021-09-03-FN1 markMCQQ.In the kinetic theory of gases, it is assumed that the gas molecules: (A) Repel each other (B) Collide elastically (C) Move with uniform velocity (D) Are massless particles
›Reveal solutionSolution
One of the founding postulates of kinetic theory is that molecular collisions are perfectly elastic, conserving kinetic energy.
Concept and Intuition
Kinetic theory models a gas as a huge number of tiny, hard particles in random motion. For the theory's predictions (like the ideal gas law and Maxwell speed distribution) to hold, the total kinetic energy of the gas must be conserved during collisions — otherwise the gas would spontaneously cool or heat as molecules collided, which isn't observed for an isolated ideal gas. Hence molecule–molecule and molecule–wall collisions are assumed perfectly elastic.
Step-by-Step Solution
- Kinetic theory postulates: molecules are point particles (negligible size compared to separation), in continuous random motion, exerting no force on each other except during collisions, and collisions (with each other and the container walls) are perfectly elastic.
- "Repel each other" is not a general assumption — intermolecular forces are neglected except at contact.
- "Move with uniform velocity" is false — molecules have a distribution of speeds and directions (Maxwell–Boltzmann distribution), each undergoing straight-line motion only between collisions.
- "Massless particles" is false — molecules have finite mass, which is essential to defining momentum, pressure, and kinetic energy in the theory.
- The correct postulate among the options is that molecular collisions are elastic.
Common Mistakes
- Confusing negligible molecular size with molecules being massless — the theory needs finite mass for momentum transfer (pressure), it only neglects the volume occupied by molecules.
✓Final answerThe correct option is (B) — Collide elastically.
ANSWER: B
- AP EAPCET 2021Set eng-2021-10-05-FN1 markMCQQ.Temperature determines the direction of net change of ___________ (A) gross Kinetic energy (B) gross Potential energy (C) intermolecular Potential energy (D) intermolecular Kinetic energy
›Reveal solutionSolution
Temperature reflects the average kinetic energy of random molecular motion; it is this intermolecular kinetic energy whose net exchange between bodies (heat flow) is dictated by temperature difference.
Concept and Intuition
Microscopically, temperature is a measure of the average kinetic energy of the disordered, random motion of molecules (translational, and to some extent rotational/vibrational) — not any ordered, bulk ('gross') motion of the object as a whole, and not the potential energy stored in intermolecular bonds/configuration. When two bodies at different temperatures are placed in contact, energy flows (as heat) in the direction that equalizes this molecular kinetic energy, always from the hotter (higher average molecular KE) to the colder body, until thermal equilibrium is reached. This is precisely the microscopic content of the zeroth and second laws: temperature — not total internal energy or potential energy — determines the direction of net thermal energy transfer.
Step-by-Step Solution
- Recognize that gross (bulk) kinetic/potential energy refers to a body's overall, macroscopic mechanical energy (e.g. a moving block), which is unrelated to temperature.
- Recognize that intermolecular potential energy relates to bonding/configuration between molecules (relevant to phase changes, not to the direction of heat flow between two bodies at different temperatures).
- Temperature, by the kinetic theory of matter, is proportional to the average kinetic energy of random molecular motion, i.e. intermolecular kinetic energy in the sense of the disordered thermal motion between molecules.
- It is exactly this quantity whose net transfer between two bodies in thermal contact is governed by their temperature difference — heat flows from higher to lower temperature until this molecular kinetic energy equalizes.
Common Mistakes
- Confusing gross (bulk, ordered, macroscopic) kinetic energy with the microscopic, random molecular kinetic energy that temperature actually measures.
- Attributing the direction of heat flow to potential energy differences rather than kinetic energy (thermal agitation).
✓Final answerThe correct option is (D) — intermolecular Kinetic energy.
ANSWER: D
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