Explain why (a) there is no atmosphere on moon. (b) there is fall in temperature with altitude.

NCERT Exemplar · Q27

Q. Explain why

(a) there is no atmosphere on moon.

(b) there is fall in temperature with altitude.

Puducherry CbseLong· 3mImportance★★★★★est

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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.

Note

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:

\text{Average kinetic energy per molecule} = \frac{3}{2} k_B T

where $k_B$ is Boltzmann's constant ( $1.38 \times 10^{-23} \, \text{J/K}$ ) 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 = \frac{1}{3} N m \overline{v^2} = N k_B T

where $P$ is pressure, $V$ is volume, $N$ is the number of molecules, $m$ is the mass of one molecule, and $\overline{v^2}$ is the mean square speed.

PV = nRT

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. …

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Both phenomena are explained by the kinetic theory of gases and the nature of thermal radiation.

The Moon lacks an atmosphere because its escape velocity is too low to retain gas molecules against thermal motion.
Temperature falls with altitude in the troposphere because the atmosphere is heated from below by the Earth's surface, not directly by sunlight.

The Core Idea: Two Different Mechanisms

These two questions might seem unrelated, but they both hinge on how gases behave under gravity and how heat is transferred. One is about whether a planet can hold onto its air, the other about how that air is warmed.

Let's take them one at a time.

(a) Why there is no atmosphere on the Moon

1. The escape velocity problem. Every celestial body has an escape velocity — the minimum speed an object needs to break free from its gravitational pull. For the Moon, this is only about $2.38 \text{ km/s}$ . For Earth, it's $11.2 \text{ km/s}$ . That's a huge difference.

2. Gas molecules are always moving. According to the kinetic theory of gases, the average speed of a gas molecule depends on temperature and molecular mass:

v_{\text{rms}} = \sqrt{\frac{3kT}{m}}

where $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is the molecule's mass. Lighter molecules (like hydrogen, helium) move faster; heavier ones (like oxygen, nitrogen) move slower.

3. The critical ratio. A planet can retain a gas only if the escape velocity is at least 6 times the root-mean-square speed of that gas molecule. This is the Jeans escape criterion. On the Moon, even at its moderate daytime temperature ( $\sim 400 \text{ K}$ ), the rms speed of nitrogen molecules is about $0.6 \text{ km/s}$ — and $6 \times 0.6 = 3.6 \text{ km/s}$ , which is greater than the Moon's escape velocity of $2.38 \text{ km/s}$ .

Watch out

A common mistake is to think the Moon has no atmosphere because it has no magnetic field. While that affects how solar wind strips away ions, the primary reason is simply gravity being too weak to hold gas molecules in the first place. Even without solar wind, any primordial atmosphere would have boiled away over geological time.

4. The result. Any gas that might have existed on the Moon — whether from volcanic outgassing or comet impacts — would have had molecules moving fast enough to simply drift off into space. The Moon is too small and too light to hold an atmosphere.

(b) Why temperature falls with altitude

1. The common misconception. Many students think "higher up means closer to the Sun, so it should be hotter." That's wrong. The Sun's radiation travels through the atmosphere almost without heating it directly — the air is mostly transparent to visible light.

2. The real heating mechanism. The Earth's surface absorbs sunlight and warms up. That warm surface then emits infrared radiation (thermal radiation). The atmosphere is opaque to much of this infrared radiation (thanks to greenhouse gases like CO₂ and water vapour), so it absorbs this energy and gets heated from below.

Tip

Think of the atmosphere as a blanket. The ground is the hot water bottle, and the air is the blanket. The part of the blanket closest to the bottle is warmest; the outer edge is coolest. That's exactly what happens in the troposphere — the lowest 10–15 km of the atmosphere. …

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Q.Explain why

The Core Idea: Two Different Mechanisms

(a) Why there is no atmosphere on the Moon

(b) Why temperature falls with altitude

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