# NCERT Class 11 Physics Solutions: Chapter 13 – Kinetic Theory-Part 3

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**Question 13.6:**

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapor and other constituents) in a room of capacity at a temperature of and pressure.

**Answer:**

Volume of the room,

Temperature of the room,

Pressure in the room,

The ideal gas equation relating pressure Volume and absolute temperature can be written as:

Where,

is Boltzmann constant

is the number of air molecules in the room

Therefore, the total number of air molecules in the given room is

**Question 13.7:**

Estimate the average thermal energy of a helium atom at

Room temperature

The temperature on the surface of the Sun

The temperature of Kelvin (the typical core temperature in the case of a star).

**Answer:**

At room temperature,

Average thermal energy

Where is Boltzmann constant

Hence, the average thermal energy of a helium atom at room temperature

On the surface of the sun,

Average thermal energy

Hence, the average thermal energy of a helium atom on the surface of the sun is .

At temperature,

Average thermal energy

Hence, the average thermal energy of a helium atom at the core of a star is

**Question 13.8:**

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not, in which case is the largest?

**Answer:**

Yes. All contain the same number of the respective molecules.

No. The root mean square speed of neon is the largest

**Explanation:**

Since the three vessels have the same capacity, they have the same volume.

Hence, each gas has the same pressure, volume, and temperature.

According to Avogadro’s law, the three vessels will contain an equal number of the respective molecules. This number is equal to Avogadro’s number,

The root mean square speed) of a gas of mass, and temperature is given by the relation:

Where, is Boltzmann constant

For the given gases are constants.

Hence depends only on the mass of the atoms, i.e.,

Therefore, the root mean square speed of the molecules in the three cases is not the same.

Among neon, chlorine, and uranium hexafluoride, the mass of neon is the smallest.

Hence, neon has the largest root mean square speed among the given gases.