Kinetic Theory Test

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Kinetic Theory Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

If the number of molecules in a gas is N then the number of molecules moving in negative X-direction will be :

A
N/6

B
N/4

C
N/3

D
N

Solution

Equal number of molecules move in each of the 6(+X,-X,+Y,-Y,+Z,-Z) directions.
Hence, number of molecules moving in -X direction = $$\frac { N }{ 6 } $$
Hence, option A is correct
Question 2
1 / -0

At what temperature will the kinetic energy of gas molecules be double of its value at 27$$^o$$C?

A
$$54^oC$$

B
$$108^oC$$

C
$$300^oC$$

D
$$327^oC$$

Solution

Kinetic energy of gas $$ (E) = \dfrac {3}{2} \times k \times T $$
Then
$$ \dfrac {E}{T} = k $$
where $$k$$ is Boltzmann constant
$$ \dfrac{{E_1}}{{T}_{1}} = \dfrac{{E}_{2}}{{T}_{2}} $$
Given
$$ E_{1} = E $$ ; $$ E_{2} = 2\times E $$ ; $$ T_{1}= 27^{o}C = 300 K $$ ; $$ T_{2}=? $$

Then $$ T_{2}=E_{2} \times \dfrac{T_{1}}{E_{1}}=2\times E \times \dfrac{300}{E} = 600 K$$
$$ T_{2} = 327^{o}C $$
Question 3
1 / -0

The internal energy of a monoatomic ideal gas is :

A
only kinetic

B
only potential

C
partly kinetic and partly potential

D
none

Solution

Internal energy (U) = Kinetic energy + Potential energy

For an ideal gas interatomic forces/interactions are assumed to be zero.
So, the potential energy is zero.
Hence, Total internal energy of an ideal monoatomic gas is purely kinetic.
Question 4
1 / -0

Keeping the number of moles, volume and temperature the same, which of the following are the same for all ideal gases?

A
rms speed of molecules

B
Density

C
Pressure

D
Average magnitude of momentum

Solution

We have the relation PV=nRT (ideal gas equation)
by keeping the number of moles, volume and temperature same, pressure will also remains same ($$\because$$R is constant)
Question 5
1 / -0

Solids have :

A
definite mass

B
definite volume

C
both A & B

D
none

Solution

Solids have finite mass as well as finite volume. And shape too for that matter.
Question 6
1 / -0

Which of the following is/are true on the basis of kinetic theory of matter?

A
Solids have a definite volume and definite shape

B
Liquids have a definite volume, but no definite shape

C
Gases have no definite volume and no definite shape

D
All of the above

Solution

(a) Solids have a definite volume and definite shape.
The particles that make up a solid are packed very closely together. In addition, each particle is tightly fixed in one position. This fixed, closely packed arrangement of particles causes a solid to have a definite shape and volume.
(b) Liquids have a definite volume, but no definite shape.
Liquid molecules are also packed closely together, but there is enough space between the molecules to allow them to slide past each other. This sliding action prevents the liquid from taking a shape of its own. As a result, liquids take the shape of the container that holds them.
(c) Gases have a no definite volume and no definite shape.
Gas molecules have either very weak bonds or no bonds at all, so they can move freely and quickly. Because of this, not only will a gas conform to the shape of its container, it will also expand to completely fill the container. Gas molecules have enough kinetic energy such that the effect of intermolecular forces is small (or zero, for an ideal gas), and they are spaced very far apart from each other; the typical distance between neighbouring molecules is much greater than the size of the molecules themselves.
Question 7
1 / -0

The amount of heat required to heat 1 mol of a monoatomic gas from 200$$^o$$C to 250$$^o$$C will be ............. if the heat required to heat the diatomic gas from 200$$^o$$C to 300$$^o$$C is Q.

A
2Q/3

B
3Q/5

C
3Q/10

D
2Q/5

Solution

The heat required is given by formulae:
$$Q= nc(T_2-T_1)$$
For monoatomic:
$$Q_1=1\times3/2R\times (250-200)=3/2R\times 50$$
For diatomic:
$$Q=1\times 5/2R(300-200)=5/2R\times 100$$
$$Q_1/Q=3\times50/5\times100$$
$$Q_1/Q=3/10$$
$$Q_1=3Q/10$$
Question 8
1 / -0

On the basis of kinetic theory of matter :

A
the solids have a definite volume and definite shape

B
the liquids have a definite volume but no definite shape

C
the gases have no definite volume and no definite shape

D
all of the above

Solution

(a) Why the solids have a definite volume and definite shape?
The particles that make up a solid are packed very closely together. In addition, each particle is tightly fixed in one position. This fixed, closely packed arrangement of particles causes a solid to have a definite shape and volume.

(b) Why the liquids have a definite volume and but no definite shape?
Liquid molecules are also packed closely together, but there is enough space between the molecules to allow them to slide past each other. This sliding action prevents the liquid from taking a shape of its own. As a result, liquids take the shape of the container that holds them. The particles in liquids are much farther apart than the particles in solids, and they're also moving around much more . Even though the particles are farther apart in liquids than in solids, some particles in liquids may still be near each other, clumped together in small groups. Because the particles are farther apart in liquids, the attractive forces among them aren't as strong as they are in solids which is why liquids don't have a definite shape. However, these attractive forces are strong enough to keep the substance confined in one large mass instead of going all over the place.
Question 9
1 / -0

The inter-molecular spaces in a liquid is :

A
less than a solid

B
more than a gas

C
more than a solid

D
more than a solid and a gas

Solution

We know that the liquid have a relatively higher intermolecular space than the solids.
Due to this the molecules of the liquid are free to move about any direction and therefore they take the shape of the container in which they are kept.
So, liquids have no definite shape but have definite volume
Question 10
1 / -0

The correct relation connecting the universal gas constant (R), Avogadro number N$$_A$$ and Boltzmann constant (K) is :

A
$$R = NK^2$$

B
$$K = NR$$

C
$$N = RK$$

D
$$R=NK$$

Solution

Units of R, N and K are $$ Joule \times mole^{-1} \times K^{-1} $$, $$ mole^{-1} $$ and $$Joule \times K^{-1}$$
So $$ R = N \times K $$

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Kinetic Theory Test - 14

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Kinetic Theory Test - 14

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Question 1

N/6

N/4

N/3

N

Solution

Question 2

$$54^oC$$

$$108^oC$$

$$300^oC$$

$$327^oC$$

Solution

Question 3

only kinetic

only potential

partly kinetic and partly potential

none

Solution

Question 4

rms speed of molecules

Density

Pressure

Average magnitude of momentum

Solution

Question 5

definite mass

definite volume

both A & B

none

Solution

Question 6

Solids have a definite volume and definite shape

Liquids have a definite volume, but no definite shape

Gases have no definite volume and no definite shape

All of the above

Solution

Question 7

2Q/3

3Q/5

3Q/10

2Q/5

Solution

Question 8

the solids have a definite volume and definite shape

the liquids have a definite volume but no definite shape

the gases have no definite volume and no definite shape

all of the above

Solution

Question 9

less than a solid

more than a gas

more than a solid

more than a solid and a gas

Solution

Question 10

$$R = NK^2$$

$$K = NR$$

$$N = RK$$

$$R=NK$$

Solution

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