**Notes**
**Assignments**
**Revision Notes**
## Multiple choice questions with one or more answer

**Question 1**. Let A & B are two sample of ideal gases of equal mole .let T be the temperature of both the gas Let E

_{A} and E

_{B} are there total energy respectively .Let M

_{A} and M

_{B} are these respective molecular mass .which of these is true

a, E

_{A} >E

_{B}
b, E

_{A} < E

_{B}
c, E

_{A} =E

_{B}
d, none of these

Solution
E_{A} = 3/2 nRT

E_{B} = 3/2 nRT

So E_{A} =E_{B}

**Question 2**. An Ideal gas undergoes an state change according to PV diagram. what is the value V

_{x}
a, V

_{0}/ 2

b, V

_{0}
c, 2V

_{0}
d, V

_{0}/ 4

Solution
As the temperature is constant PV = constant

2P_{0} V_{x} = P_{0}V_{0}

V_{x} = V_{0}/ 2

## Linked Comprehensions type

A container contains N

_{2} gas at T K. The no of moles of gas is n

_{0}. Consider it behaves like ideal gas. It rms speed is v

_{0}
**Question 3**.What is the total translational kinetic energy

a, (3/2 )n

_{0}RT

b, 3/2 RT

c, 1/2 RT

d, (1/2) n

_{0}RT

Solution
KE = (3/2) nRT

= (3/2) n_{0}RT

**Question 4**.Suppose the temperature of gas is tripled and N

_{2} molecules dissociate into atom. Then what will be the rms speed of atom.

a, v

_{0}√6

b. √(6 v

_{0})

c, v

_{0}√3

d, √(3 v

_{0})

Solution
v_{0} = √3KT/M

v_{t} = √9KT/(M/2)

=v_{0}√6

**Question 5**.if V

_{p} denotes most probable velocity of N

_{2} at T then which of these is correct

a, V

_{p} : V

_{0}= √2 : √3

b, V

_{p} : V

_{0} = 1 : 1

c, V

_{p} : V

_{0} = 2 : 3

d, V

_{p} : V

_{0} = √2 : 3

Solution
V_{p} = √2kT/M

= √2/3 x 3kT/M

= V_{0}√(2/3)

## Multiple choice questions with one or more answer

**Question 6** An ideal gas undergoes the process describe by equation

P = P

_{0} - aV

^{2}
Where P

_{0} , a are positive constant and V is the volume of one mole of gas

Maximum temperature attainable by gas

a, 2/3 (P

_{0}/R) √(P

_{0}/3a)

b, 3 P

_{0} √P

_{0}/2Ra

c, (1/3R)√(P

_{0}/3a)

d, 4/3 (P

_{0}/R)√(P

_{0}/2)

Solution
P = P_{0} - aV^{2}

= P_{0}-a(RT/P)^{2}

PV = RT for one mole of gas

T = (1/R√a )P√(P_{0} -P)

= (1/R√a )√(P_{0}P^{2} - P^{3})

For T_{max}

d (P_{0}P^{2} - P^{3}) /dP= 0

P = 2P_{0}/3

Putting this value

T_{max} = 2/3 (P_{0}/R) √(P_{0}/3a)

**Question 7**. Let V, V

_{rms} and V

_{p} respectively denotes the mean speed, root mean square speed and most probable speed of the molecule in ideal monoatomic gas at absolute temperature T. The mass of the molecule

is m then

A, No molecule can have a speed greater the (2)

^{1/2}V

_{rms}
B, No molecule can have a speed less the V

_{p} / (2)

^{1/2}
C, V

_{p} < V < V

_{rms}
D, The average kinetic charge of a molecule (3/4 )mV

_{p}^{2}
Solution
V_{rms}= (3kT/M)^{1/2}

V = (8KT/πM)^{1/2}

V_{p}= (2KT/M)^{1/2}

So it is clear

V_{p} < V < V_{rms}

Also

Average kinetic energy

=(½)mV_{rms}^{2}

V_{rms}^{2} = 3KT/M

V_{p}^{2} = 2KT/M

V_{rms}^{2} = 3/2 V_{p}^{2}

So E=3/4 V_{p}^{2}

So Ans. C&D

## Linked Comprehensions type

A flask contains Oxygen, Hydrogen & chlorine in the ration of 3:2:1 mixture at 27 °C

Molecular mass of Oxygen = 32

Molecular mass of Hydrogen = 2

Molecular mass of Chlorine = 70.9

**Question 8**.Find the ratio of average kinetic energy per molecule of Oxygen & Hydrogen

1, 1:2

2, 1:1

3, 1:16

4, 2:1

**Question 9**.find the ratio of average kinetic energy per molecule of Hydrogen & chlorine

1, 1:2

2, 1:1

3, 1:16

4, 1:1

Solution 8-9
All the molecule have same kinetic energy at same temperature

**Question 10**.find the ratio of mean speed of Oxygen, chlorine, Hydrogen

a, 4:1 : (.45)

^{1/2}
b, 5:2 :(5)

^{1/2}
c, 1: (.45)

^{1/2}:4

d, 2 :(.45)

^{1/2} : (1.5)

^{1/2}
Solution
V= (8KT/πM)^{1/2}

V_{H}= (8KT/πM_{H})^{1/2}

V_{O}= (8KT/πM_{O})^{1/2}

V_{CL}= (8KT/πM_{CL})^{1/2}

V_{O} : V_{CL}: V_{H} = (8KT/πM_{O})^{1/2} : (8KT/πM_{CL})^{1/2}: (8KT/πM_{H})^{1/2}

= 1/(M_{O}) ^{1/2}: 1/(M_{CL})^{1/2} : 1/(M_{H}) ^{1/2}

= 1: (.45)^{1/2}:4

## Multiple choice questions with one or more answer

**Question 11**.Suppose a container is evacuated to have just one molecule of a gas in it. Let V

_{a} & V

_{rms} represent the average speed and rms speed of the molecule

a) V

_{a} > V

_{rms}
b) V

_{a} < V

_{rms}
c) V

_{a} = V

_{rms}
d) V

_{rms} is undefined

Solution
. average speed is define

V_{a} = ∑V / N

= V/1 = V

mean square speed = ∑ V^{2} / N

= V^{2}

root mean square = (∑ V^{2} / N)^{1/2}= V

So V_{a} = V_{rms}

**Question 12**. The velocities of the molecules are v, 2v, 3v, 4v & 5v. The rms speed will be

a, 11v

b, v(11)

^{1/2}
c, v

d, 3.3v

Solution
Vrms= (∑ V^{2} / N)^{1/2}

= [(V^{2} + 4V^{2} + 9V^{2} + 16V^{2} + 25V^{2})/5]^{1/2}

=v(11)^{1/2}

**Question 13**.Equal Number of molecules of hydrogen & Oxygen are contained in a vessel at one atmosphere

pressure. The ratio of the collision frequency of hydrogen molecules to the of Oxygen molecules on the

container

a,1:4

b,4:1

c, 1:16

d, 16:1

Solution
n_{1} = Vrms / 2L ---Hydrogen

n_{2} = Vrms/2L ---Oxygen

n_{1}/n_{2} = Vrms of Hydrogen/ Vrms of oxygen

Vrms of Hydrogen/ Vrms of oxygen = (M_{O}/M_{H})^{1/2}

So n_{1}/n_{2} = 4:1

**Question 14**.The prefect gases A, B & C having masses m

_{1}, m

_{2}& m

_{3} at temperature T

_{1}, T

_{2} & T

_{3} are mixed without any loses of internal energy of the molecules. The molecules weight of the gases is M

_{1}, M

_{2}, M

_{3} what

is the final temperature of mixture.

a, [(m

_{1}/M

_{1})T

_{1} + (m

_{2}/M

_{2})T

_{2} + (m

_{3}/M

_{3})T

_{3}]/(m

_{1}/M

_{1}+m

_{2}/M

_{2}+m

_{3}/M

_{3})

C, [(M

_{1}/m

_{1})T

_{1} + (M

_{2}/m

_{2})T

_{2} + (M

_{3}/m

_{3})T

_{3}]/(M

_{1}/m

_{1}+M

_{2}/m

_{2}+M

_{3}/m

_{3})

b, [(m

_{1})T

_{1} + (m

_{2})T

_{2} +(m

_{3})T

_{3}]/(m

_{1}+m

_{2}+m

_{3})

d, [(M

_{1})T

_{1} + (M

_{2})T

_{2} + (M

_{3})T

_{3}]/(M

_{1}+M

_{2}+M

_{3})

Solution

Internal kinetic energy

= (3/2) nRT

so for A KE_{1} = (3/2 )(m_{1}/M_{1}) RT_{1},

for B KE_{2} = (3/2 )(m_{2}/M_{2}) RT_{2},

for C KE_{3} = (3/2 )(m_{3}/M_{3}) RT_{3},

Now final Kinetic energy

KE = 3/2 (m_{1}/M_{1}+m_{2}/M_{2}+m_{3}/M_{3}) RT

Now

KE = KE_{1} + KE_{3}+KE_{3}

T = [(m_{1}/M_{1})T_{1} + (m_{2}/M_{2})T_{2} + (m_{3}/M_{3})T_{3}]/(m_{1}/M_{1}+m_{2}/M_{2}+m_{3}/M_{3})

**Question 15**. An ideal gas under goes an process show in Pv diagram.

Which of the diagram represent it on V-T diagram

a.

b.

c.

d.

Solution
In A to B process

P =constant

so PV = nRT

V is proportional to T

so volume should increase with temp.

In B to C

V = Const

PV = nRT

P is proportional to T

So pressure increase, temperature increases

**Question 16** A gas mixture consist of molecules of type A, B, C, D with molecular

masses M

_{a} > M

_{b} > M

_{c} >M

_{d}
Two statement are drawn from it

**Statement A**, Average kinetic energy of four type of gases in the mixture are in the ratio

E

_{a}/1 =E

_{b}/1 =E

_{c}/1 =E

_{d}/1

**Statement B**, Rms speed of molecules of the four types are in the order if V is the rms speed

V

_{D} > V

_{C} > V

_{C} > V

_{A}
which one of following is true

a, Only A correct

b, Only B correct

c, A & B both are correct

d, A & B both are wrong

Solution
Average kinetic energy is same for all the gases at the same temperature

rms speed is inversely proportional to the Molecular mass of the gas

since M_{a} > M_{b} > M_{c} >M_{d}

V_{D} > V_{C} > V_{C} > V_{A}

**Question 17**. There are two statement

**Statement A**. Equal volumes of all gases at the same temperature T and pressure P contain an equal no of Molecules

**Statement B**,.the no of molecules in one mole of any gas is 6.0255 * 10

^{22}.

which one of the following is correct

a. A and B both

b. A only

c B only

d. A and B both are incorrect

Solution
Statement A is Avogadro law. So true

Avogadro no is 6.0255 * 10^{23 } So second one is true

**Question 18**.There are two statement about Ideal gases

**Statement A** The V

_{rms} of gas molecules depends on the mass of the gas molecule and the temperature

**Statement B** The V

_{rms} is same for all the gases at the same temperature

which one of the following is correct

a. A and B both

b. A only

c. B only

d. A and B both are incorrect

Solution
v_{rms} depends on mass and temperature

So A is correct . Ans B is incorrect

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Class 11 Maths
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