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**Question 13.1** Estimate the fraction of molecular volume to the actual volume occupied by oxygen
gas at STP. Take the diameter of an oxygen molecule to be 3 Å.

**Question 13.2** Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard
temperature and pressure (STP : 1 atmospheric pressure, 0 °C). Show that it is 22.4
litres.

**Question 13.3** Figure13.8 shows plot of PV/T versus P for 1.00×10–3 kg of oxygen gas at two
different temperatures.

(a) What does the dotted plot signify?

(b) Which is true: T1 > T2 or T1 < T2?

(c) What is the value of PV/T where the curves meet on the y-axis?

(d) If we obtained similar plots for 1.00×10–3 kg of hydrogen, would we get the same
value of PV/T at the point where the curves meet on the y-axis? If not, what mass
of hydrogen yields the same value of PV/T (for low pressurehigh temperature
region of the plot) (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u,
R = 8.31 J mo1–1 K–1.)

**Question 13.4** An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and
a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge
pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of
oxygen taken out of the cylinder (R = 8.31 J mol–1 K–1, molecular mass of O2 = 32 u).

**Question 13.5** An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a
temperature of 12 °C. To what volume does it grow when it reaches the surface,
which is at a temperature of 35 °C ?

**Question 13.6** Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water
vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of
27 °C and 1 atm pressure.

**Question 13.7** Estimate the average thermal energy of a helium atom at (i) room temperature
(27 °C), (ii) the temperature on the surface of the Sun (6000 K), (iii) the temperature
of 10 million kelvin (the typical core temperature in the case of a star).

**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 vrms the largest ?

**Question 13.9** At what temperature is the root mean square speed of an atom in an argon gas
cylinder equal to the rms speed of a helium gas atom at – 20 °C ? (atomic mass of Ar
= 39.9 u, of He = 4.0 u).

**Question 13.10** Estimate the mean free path and collision frequency of a nitrogen molecule in a
cylinder containing nitrogen at 2.0 atm and temperature 17 0C. Take the radius of a
nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the
molecule moves freely between two successive collisions (Molecular mass of N2 =
28.0 u).

**Question 13.11** A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm
long mercury thread, which traps a 15 cm column of air. What happens if the tube
is held vertically with the open end at the bottom ?

**Question 13.12** From a certain apparatus, the diffusion rate of hydrogen has an average value of
28.7 cm3 s–1. The diffusion of another gas under the same conditions is measured to
have an average rate of 7.2 cm3 s–1. Identify the gas.
[Hint : Use Graham’s law of diffusion: R1/R2 = ( M2 /M1 )1/2, where R1, R2 are diffusion
rates of gases 1 and 2, and M1 and M2 their respective molecular masses. The law is
a simple consequence of kinetic theory.]

**Question 13.13** A gas in equilibrium has uniform density and pressure throughout its volume. This
is strictly true only if there are no external influences. A gas column under gravity,
for example, does not have uniform density (and pressure). As you might expect, its
density decreases with height. The precise dependence is given by the so-called law
of atmospheres
n2 = n1 exp [ -mg (h2 – h1)/ kBT]
where n2, n1 refer to number density at heights h2 and h1 respectively. Use this
relation to derive the equation for sedimentation equilibrium of a suspension in a
liquid column:
n2 = n1 exp [ -mg NA (ρ - P′ ) (h2 –h1)/ (ρ RT)]
where ρ is the density of the suspended particle, and ρ’ that of surrounding medium.
[NA is Avogadro’s number, and R the universal gas constant.] [Hint : Use Archimedes
principle to find the apparent weight of the suspended particle.]

**Question 13.14** Given below are densities of some solids and liquids. Give rough estimates of the
size of their atoms : [Hint : Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use
the known value of Avogadro’s number. You should, however, not take the actual
numbers you obtain for various atomic sizes too literally. Because of the crudeness
of the tight packing approximation, the results only indicate that atomic sizes are in
the range of a few Å].

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- Chapter 3: Motion in a Straight Line
**[Ques wise Ans]** - Chapter 1 Physical World
- Chapter 2 Units and Measurement
- Chapter 3 Motion in a Straight Line
- Chapter 4 Motion in a Plane
- Chapter 5 Laws of Motion
- Chapter 7 Systems of Particles and Rotational Motion
- Chapter 6 Work Energy and Power
- Chapter 8 Gravitation
- Chapter 9 Mechanical Properties of Solids
- Chapter 10 Mechanical Properties of Fluids
- Chapter 11 Thermal Properties of Matter
- Chapter 12 Thermodynamics
- Chapter 13 Kinetic Theory
- Chapter 14 Oscillations
- Chapter 15 Waves

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