Kinetic Theory Test

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Kinetic Theory Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

The deviation of gases from the behaviour of ideal gas is due to :

A
colourless molecules

B
covalent bonding of molecules

C
attraction of molecules

D
absolute scale of temperature

Solution

For ideal behaviour we assume there is no attractive force between molecules of gas but there is an attractive force which produces non ideality.
Hence, option(C)
Question 2
1 / -0

Pressure exerted by a perfect gas is equal to :

A
mean kinetic energy per unit volume

B
half of mean kinetic energy per unit volume

C
two third of mean kinetic energy per unit volume

D
one third of mean kinetic energy per unit volume

Solution

Pressure exerted by ideal gas, per unit volume:
$$P_{unit \ volume} = nRT$$
Mean Kinetic energy per unit volume $$= \dfrac{3}{2} nRT$$
i.e.
Pressure per unit volume is two third of the mean kinetic energy.
Option C is correct.
Question 3
1 / -0

The nature of the graph of pressure 'P' against reciprocal of volume 'V' of an ideal gas at constant temperature is

A
a straight line not passing through origin

B
a parabola

C
a straight line passing through origin

D
a rectangular hyperbola

Solution

Boyle's Law states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system.
By plotting pressure (p) against the reciprocal of the volume (1/V) a straight line is obtained the gradient of which is the constant in Boyle’s Law.
Question 4
1 / -0

Kinetic energy of a gas molecule depends on:

A
Pressure

B
Volume

C
Temperature

D
All the above

Solution

According to kinetic theory, "The average kinetic energy of gas molecules depends upon the absolute temperature". At any given temperature, the molecules of all gases have the same average kinetic energy.
Option C is correct.
Question 5
1 / -0

A polyatomic gas with n degrees of freedom has a mean energy per molecules given by :

A
$$\displaystyle \frac{n}{2}\, RT$$

B
$$\displaystyle \frac{1}{2}\, RT$$

C
$$\displaystyle \frac{n}{2}\, kT$$

D
$$\displaystyle \frac{1}{2}\, kT$$

Solution

Mean energy of gas per degree of freedom $$=\dfrac{1}{2}kT$$
where $$k$$ is the Boltzmann constant.
Thus mean energy of gas with $$n$$ degrees of freedom $$=\dfrac{n}{2}kT$$
Question 6
1 / -0

The mean kinetic energy of a perfect mono atomic gas molecule at the temperature $$T^{o}K$$ is :

A
$$\displaystyle\ \frac{1}{2}kT$$

B
$$kT$$

C
$$\displaystyle\ \frac{3}{2}kT$$

D
$$2kT$$

Solution

A monoatomic gas has 3 degrees of freedom, one each along for each axis (translation motion).
The kinetic energy per molecule per degree of freedom is $$\dfrac{1}{2}kT$$
i.e.
The kinetic energy per molecule for a monoatomic gas is $$\dfrac{3}{2}kT$$
Hence option C is correct.
Question 7
1 / -0

The number of degrees of freedom for each atom of a monoatomic gas is :

A
3

B
5

C
6

D
1

Solution

A monoatomic gas has 3 degrees of freedom for translation motion.
Hence, option A is correct.
Question 8
1 / -0

The perfect gas equation for 4 gram of hydrogen gas is :

A
$$PV=RT$$

B
$$PV= 2RT$$

C
$$PV$$ = $$\displaystyle\ \frac{1}{2} RT$$

D
$$PV = 4RT$$

Solution

$$n$$ = $$\displaystyle\ \frac{4}{2} = 2$$ (number of moles)
$$\Rightarrow PV=2RT$$
Question 9
1 / -0

When a solid object is heated, the molecules that make up the object:

A
Begin to vibrate faster

B
Lose energy

C
Make frequent collisions

D
Both A and C

Solution

When a solid object is heated, the molecules that make up the object begin to vibrate faster, they also start making frequent collisions.
Hence, option D is correct.
Question 10
1 / -0

The average kinetic energy of a molecule of a perfect gas is :

A
$$\dfrac{2}{3}k T$$

B
$$1.5kT$$

C
$$2.5kT$$

D
none of these

Solution

Average kinetic energy of a molecule is given by:
$$K.E = \frac{3}{2}kT = 1.5kT$$
Where k is the Boltzmann constant.
Hence option B is correct,

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Kinetic Theory Test - 15

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Kinetic Theory Test - 15

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SHARING IS CARING

Question 1

colourless molecules

covalent bonding of molecules

attraction of molecules

absolute scale of temperature

Solution

Question 2

mean kinetic energy per unit volume

half of mean kinetic energy per unit volume

two third of mean kinetic energy per unit volume

one third of mean kinetic energy per unit volume

Solution

Question 3

a straight line not passing through origin

a parabola

a straight line passing through origin

a rectangular hyperbola

Solution

Question 4

Pressure

Volume

Temperature

All the above

Solution

Question 5

$$\displaystyle \frac{n}{2}\, RT$$

$$\displaystyle \frac{1}{2}\, RT$$

$$\displaystyle \frac{n}{2}\, kT$$

$$\displaystyle \frac{1}{2}\, kT$$

Solution

Question 6

$$\displaystyle\ \frac{1}{2}kT$$

$$kT$$

$$\displaystyle\ \frac{3}{2}kT$$

$$2kT$$

Solution

Question 7

3

5

6

1

Solution

Question 8

$$PV=RT$$

$$PV= 2RT$$

$$PV$$ = $$\displaystyle\ \frac{1}{2} RT$$

$$PV = 4RT$$

Solution

Question 9

Begin to vibrate faster

Lose energy

Make frequent collisions

Both A and C

Solution

Question 10

$$\dfrac{2}{3}k T$$

$$1.5kT$$

$$2.5kT$$

none of these

Solution

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