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11th Physics Weekly Test - 3 ( Kinetic Theory of Gases )

MABS Institution

11th Physics Weekly Test - 3 ( Kinetic Theory of Gases )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

Two vessels have equal volumes. One of them contains hydrogen at one atmosphere and the other helium at two atmospheres. If both the samples are at the same temperature, the rms velocity of the hydrogen molecules is _________.

equal to that of the helium molecules
twice that of the helium molecules
half that of the helium molecules
\(\sqrt 2\) times that of the helium molecules

The KE. of one mole of a gas at normal temperature and pressure is (R = 8.31 J mol^-1 K^-1)_________.

0.56 x 10⁴ J
1.3 x 10² J
2.7 x 10² J
3.4x10³ J

The kinetic theory of gases breaks down most at _________.

low pressure and high temperature
high pressure and low temperature
low pressure and low temperature
high pressure and high temperature

Match and choose the correct answer

a) Average kinetic energy per degree of freedom - i) 6

b) The number of degrees of freedom due to translational motion of oxygen - ii) 1/2 KT

c) The number of degrees of freedom of H₂O - iii) Charles's law

d) Volume is proportional to temperature - iv) 2

i) ii) iii) iv)
iv) iii) ii) i)
ii) iv) i) iii)
ii) i) iv) iii)

Oxygen and hydrogen gases are at the same temperature the ratio of the average K.E of an oxygen molecule and that of a hydrogen molecule is

16
4
1
\(\frac{1}{4}\)

The tempetature at which the KE of a gas molecules is double its value at 27°C is

54°C
300 K
327°C
108°C

Four molecules have speed 2 km/s, 3 km/s, 4 km/s and 5 km/s. The rms speed of these molecules in km/s is ________

\(\sqrt\frac{27}{2}\)
\(\sqrt{27}\)
2\(\sqrt{27}\)
\(\sqrt{54}\)

The perfect gas equation can be written as

PV = \(\mu\)RT
PV = \(\mu\)R
PV = RT
P = \(\mu\)RTV

Ajar has mixture of hydrogen and Oxygen gases in the ratio 1 : 5. The ratio of mean kinetic energies of hydrogen and Oxygen molecules is ________.

1: 5
5: 1
1: 1
1: 25

The temperature is changed from 27°C to 327°C. Find ratio of K.E of molecules at two temperature.

3:2
2:3
1:2
2:1

In an adiabatic change, the pressure and temperature of a mono - atomic gas are related as p x T^C, where C equals

\(\frac{2}{5}\)
\(\frac{5}{2}\)
\(\frac{3}{5}\)
\(\frac{5}{3}\)

Which of the following statement/statements are correct?

i) Pressure of the gas molecules increases with increases of number density

ii) Pressure decreases with increases of mean square speed of the gas molecules

iii)) larger mass of the molecule will have larger momentum for fixed speed.

i) ii)
ii) iii)
i) iii)
all are correct

A cylinder of capacity 20 litres is filled with hydrogen gas. The total average K.E. of translatory motion of its molecules is 1.5 x 10⁵ J. The pressure of hydrogen in the cylinder is ________.

2 x 10⁶Nm^-2
3 x 10⁶Nm^-2
4 x 10⁶Nm^-2
5 x 10⁶Nm^-2

Two identically sized rooms A and B are connected by an open door. If the room A is air conditioned such that its temperature is 4°C lesser than room B, which room has more air in it?

Room A
Room B
Both room has same air
Cannot be determined

For a given gas molecule at a fixed temperature, the area under the Maxwell-Boltzmann distribution curve is equal to

\(\frac{PV}{KT}\)
\(\frac{KT}{PV}\)
\(\frac{P}{NKT}\)
PV

Two different ideal gases are enclosed in two different vessels at the same pressure. If \(\rho\)₁ and \(\rho\)₂ are their densities and v₁ and v₂ their rrns speeds, respectively then - is equal to ________.

\(\frac { { \rho }_{ 1 }^{ 2 } }{ { \rho }_{ 2 }^{ 2 } } \\ \)
\(\frac { { \rho }_{ 2 }^{ 2 } }{ { \rho }_{ 1}^{ 2 } } \\ \)
\(\sqrt { \frac { { \rho }_{ 1 }^{ } }{ { \rho }_{ 2 }^{ } } }\)
\(\sqrt { \frac { { \rho }_{ 2 }^{ } }{ { \rho }_{ 1 }^{ } } }\)

The ratio \(\gamma =\frac { { C }_{ p } }{ { C }_{ V } } \) for a gas mixture consisting of 8 g of helium and 16 g of oxygen is

\(\frac { 23}{15}\)
\(\frac { 15}{23}\)
\(\frac { 27}{17}\)
\(\frac { 17}{27}\)

On colliding with the walls in a closed container, the ideal gas molecules.

transfer momentum to the walls
lose momentum completely
move with smaller speeds
perform Brownian motion.

A sample of gas consists of \(\mu\)₁ moles of monoatomic molecules, \(\mu\)₂ moles of diatomic molecules and \(\mu\)₃ moles of linear triatomic molecules. The gas is kept at high temperature. What is the total number of degrees of freedom?

[3\(\mu\)₁ + 7( \(\mu\)₂ + \(\mu\)₃)] N_A
[3\(\mu\)₁ + 7\(\mu\)₂ + 6\(\mu\)₃] N_A
[7\(\mu\)₁ + 3( \(\mu\)₂ + \(\mu\)₃)] N_A
[3\(\mu\)₁ + 6( \(\mu\)₂ + \(\mu\)₃)] N_A

If there are n no. of molecules per unit volume and m is the mass of each, Vx is the x - component of velocity pressure can be written as,

P= nm\({ V }_{ x }^{ 2 }\)
P= 2nm\({ V }_{ x }^{ 2 }\)
P= m\({ V }_{ x }^{ 2 }\)
P= n\({ V }_{ x }^{ 2 }\)

If the internal energy of an ideal gas U and volume V are doubled then the pressure

doubles
remains same
halves
quadruples

The temperature of an ideal gas is increased from 120 K to 480 K If at 120 K the root mean square velocity of the gas molecules is v, at 480 K it becomes

4v
2v
\(\frac{v}{2}\)
\(\frac{v}{4}\)

The ratio of the vapour densities of two gases at a gn is 9 : 8. Theratio of the r_ms velocity of their molecules is

3: 2\(\sqrt{2}\)
2\(\sqrt{2}\):3
9:8
8:9

Gas exerts pressure on the walls of the container

gas has weight
gas molecules have momentum
gas molecule collide with each other
gas molecules collide with the walls of the container

Which of the following gases will have least rms speed at a given temperature?

Hydrogen
Nitrogen
Oxygen
Carbon dioxide

The temperature of an ideal gas is increased from 27°C to 927°C. The root mean square speed of its molecules becomes.

3 times
double
4 times
6 times

The molecular weights of oxygen and hydrogen are 32 and 2, respectively. The rms velocities of their molecules at a given temperatures, will be ill the ratio

4 : 1
1 : 4
1 : 16
16 : 1

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature the ratio \(\frac { { C }_{ p } }{ { C }_{ v } } \)for the gas is

\(\frac{4}{3}\)
2
\(\frac{5}{3}\)
\(\frac{3}{2}\)

Moving with uniform speed. The temperature of the gas molecules inside will

increase
decrease
remain the same
decrease for some, while increases for others.

A container has one mole of monoatomic ideal gas. Each molecule has f degrees of freedom. What is the ratio of \(\gamma =\frac { { C }_{ p } }{ { C }_{ V } } \) ?

f
\(\frac{f}{2}\)
\(\frac{f}{f+2}\)
\(\frac{f+2}{f}\)

In dynamic equilibrium, molecules of gas collide and change their speeds during the collision

but the average properties vary
but the average properties constant
but the peak properties constant
but the rms properties constant

Pressure exerted by a gas is _______.

independent of the density of the gas
inversely proportional to the density of the gas
directly proportional to the density of the gas
directly proportional to the square of the density of the gas

If the rms speed of the molecules of a gas is 1000 ms^-1 the average speed of the molecule is

1000 ms^-1
922 ms^-1
780 ms^-1
849 ms^-1

The pressure exerted on the walls of the container by a gas is due to the fact that the gas molecules _________.

lose their K.E
Stick to the walls
are accelerated towards the walls
change their momenta due to collision with the walls.

The average KE. of a hydrogen gas molecule at STP will be (Boltzmann constant k_B 1.38 x 10^-23 JK^-1) _________.

0.186 x 10^-28 J
0.372 x 10^-20 J
0.56 x 10^-20 J
5.6 x 10^-20 J

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