Kinetic Theory Test

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Kinetic Theory Test - 38

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Question 1
1 / -0

The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000cc at sea level (pressure 1 atmosphere, temperature 27$$^o$$C). Assume that the temperature around Mount Everest is -$$73^o$$C and that the oxygen cylinder has a capacity of 5.2 litters. The pressure at which oxygen be filled (at site) in the cylinder is

A
3.86 atm

B
5.00 atm

C
5.77 atm

D
1 atm

Solution

Since moles of gas must remain constant,

$$\dfrac { { P }_{ 1 }{ V }_{ 1 } }{ { T }_{ 1 } } =\dfrac { { P }_{ 2 }{ V }_{ 2 } }{ { T }_{ 2 } } $$

$$\dfrac { 1(30000) }{ 300 } =\dfrac { P(5200) }{ 143 } $$

$$P=3.86atm$$
Question 2
1 / -0

Which of the following assumptions is/are true according to kinetic theory?

A
All matter is composed of small particles

B
The particles of matter are in constant motion

C
All collisions between the particles of matter are perfectly elastic

D
All of the above

Solution

The kinetic theory explains the differences between the three states of matter. It states that all matter is made up of moving particles which are molecules or atoms. In solids, the particles are so tightly bound to each other that they can only vibrate but not move to another location. In liquids, the particles have enough free space to move about, but they still attract one another. In gases, the particles are far apart and can move about freely since there is much free space. Solids change into liquids, and liquids into gases when the particles gain more kinetic energy, like when being heated and are able to move apart from one another. When the molecules vibrate more quickly upon heating, some of them escape from the matter.
So, the kinetic theory states that:
1. All matter is composed of small particles.
2. The particles of matter are in constant motion.
3. All collisions between the particles of matter are perfectly elastic.
Question 3
1 / -0

The top surface of a liquid behaves like stretched membrane because

A
The molecules below the top surface exert upward pressure

B
The molecules are attracted more to the sides of the containing vessel.

C
The molecules below the top surface attract the molecules above

D
none of the above

Solution

The property of $$surface$$ $$tension$$:
The molecules in the liquid experience a force which acts equally for its neighboring molecules.
However this cohesive force pulls the molecules on the surface inwards.
Due to this unbalanced force the top surface of a liquid behaves like $$ stretched $$ $$ membrane. $$
Question 4
1 / -0

Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient). When it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be :

A
$$\sqrt{2}$$

B
$$2$$ times

C
unchanged

D
half

Solution

Kinetic energy of gas molecules is $$\dfrac{3}{2}RT$$.
Thus $$\dfrac{E_f}{E_i}=\dfrac{T_f}{T_i}=\dfrac{600}{300}=2$$
Question 5
1 / -0

A gas mixture consists of 2moles of oxygen and 4moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

A
4 RT

B
15 RT

C
9 RT

D
11 RT

Solution

The internal energy of the system is given as $$U=n(\displaystyle\frac{f}{2}R)T$$. Here f is the degree of freedom which is 5 for oxygen(diatomic molecule) and 3 for argon(monoatomic molecule). Thus we get the total internal energy as $$2(\displaystyle\frac{5}{2})RT+4(\frac{3}{2})RT=11RT$$
Question 6
1 / -0

Choose the correct answer from the given options below.

Kinetic energy of the molecules ------------- with an increase in temperature

A
increases

B
decreases

C
remains the same

D
increases then decreases

Solution

Solution:
If temperature is increased then the molecules will gain energy due to which the random motion of the molecules increases. As the random motion increases , it's velocity increase which increase it's kinetic energy.
Hence option A is correct.
Question 7
1 / -0

A sample of an ideal gas occupies a volume of 'V' at a pressure 'P' and absolute temperature 'T'. The mass of each molecule is 'm'. The equation for density is

A
mkT

B
P/kT

C
P/(kTV)

D
Pm/kT

Solution

We know that PV = nRT =(m/M)RT
Where M = Molecular weight
Now $$P\times \left(\displaystyle \frac{m}{d}\right)$$ = $$\left(\displaystyle\ \frac{m}{M} \right)RT$$
where d = density of gas
$$\displaystyle\ \frac{p}{d}$$ = $$\displaystyle\ \frac{RT}{M}$$ = $$\displaystyle\ \frac{kN_{A}T}{M}$$
Where $$R$$ = $$kN_{A}$$, k is Boltzmann constant
But $$\displaystyle\ \frac{ M}{N_{A}}$$ = m = mass of each molecule so
So, $$d$$ = $$\displaystyle\ \frac{P\times m}{kT}$$
Question 8
1 / -0

If 2 mole of an ideal monatomic gas at temperature $$T_{0}$$ is mixed with 4 moles of another ideal monatomic gas at temperature $$2T_{0}$$, then the temperature of the mixture is

A
$$\displaystyle\ \frac {5}{3} T_{0}$$

B
$$\displaystyle\ \frac {3}{2} T_{0}$$

C
$$\displaystyle\ \frac {4}{3} T_{0}$$

D
$$\displaystyle\ \frac {5}{4} T_{0}$$

Solution

Let T be the temperature of the mixture, then

$$U$$ = $$U_{1}+U_{2}$$

where, $$U_1 $$ and $$U_2 $$ are the energies of the gas molecules.

$$\Rightarrow$$ $$\displaystyle\ \frac{f}{2}(n_{1}+n_{2})RT$$

$$n_1$$ and $$n_2$$ are the number of gas molecules.

$$R$$ is the universal gas constant.

$$=\displaystyle\ \frac{f}{2}(n_{1})(R)(T_{0})$$+ $$\displaystyle\ \frac{f}{2}(n_{2})(R)(2T_{0})$$

$$\Rightarrow$$ $$(2+4)T$$= $$2T_{0}+8T_{0}$$

($$\because$$ $$n_{1}=2$$ $$n_{2} =4)$$

$$\therefore$$ $$T$$=$$\displaystyle\ \frac{5}{3}T_{0}$$
Question 9
1 / -0

How many degrees of freedom are associated with 2grams of He at NTP?

A
3

B
$$3.01\times10^{23}$$

C
$$9.03\times10^{23}$$

D
6

Solution

Moles of He =$$\displaystyle\ \frac{2}{4}$$ = $$\displaystyle\ \frac{1}{2}$$
Molecules = $$\displaystyle\ \frac{1}{2}\times6.02\times10^{23}$$ = $$3.01\times10^{23}$$
As there are 3 degrees of freedom corresponding of 1 molecule of a monatomic gas.
$$\therefore$$ Total degrees of freedom = $$3\times3.01\times10^{23}$$
$$= 9.03\times10^{23}$$
Question 10
1 / -0

Kinetic theory of matter states about :

A
three states of matter

B
differences between the three states of matter

C
fourth state of matter

D
all of the above

Solution

The kinetic theory explains the differences between the three states of matter. It states that all matter is made up of moving particles which are molecules or atoms.

In solids, the particles are so tightly bound to each other that they can only vibrate but not move to another location.
In liquids, the particles have enough free space to move about, but they still attract one another.
In gases, the particles are far apart and can move about freely since there is much free space.

Solids change into liquids, and liquids into gases when the particles gain more kinetic energy,

So, the correct option is $$B$$

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Kinetic Theory Test - 38

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Kinetic Theory Test - 38

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Question 1

3.86 atm

5.00 atm

5.77 atm

1 atm

Solution

Question 2

All matter is composed of small particles

The particles of matter are in constant motion

All collisions between the particles of matter are perfectly elastic

All of the above

Solution

Question 3

The molecules below the top surface exert upward pressure

The molecules are attracted more to the sides of the containing vessel.

The molecules below the top surface attract the molecules above

none of the above

Solution

Question 4

$$\sqrt{2}$$

$$2$$ times

unchanged

half

Solution

Question 5

4 RT

15 RT

9 RT

11 RT

Solution

Question 6

increases

decreases

remains the same

increases then decreases

Solution

Question 7

mkT

P/kT

P/(kTV)

Pm/kT

Solution

Question 8

$$\displaystyle\ \frac {5}{3} T_{0}$$

$$\displaystyle\ \frac {3}{2} T_{0}$$

$$\displaystyle\ \frac {4}{3} T_{0}$$

$$\displaystyle\ \frac {5}{4} T_{0}$$

Solution

Question 9

3

$$3.01\times10^{23}$$

$$9.03\times10^{23}$$

6

Solution

Question 10

three states of matter

differences between the three states of matter

fourth state of matter

all of the above

Solution

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