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Kinetic Theory of Gases
Gas Laws
2011
A perfect gas at 27 0 C is heated at constant pressure so as to double its volume. The
co
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1.
increase in temperature of the gas will be
a) 6000 C
c) 540 C
d) 3000 C
Air inside a closed container is saturated with water vapour. The air pressure is p
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2.
b) 327 0 C
and the saturated vapour pressure of water is p . If the mixture is compressed to onehalf of its volume by maintaining temperature constant, the pressure becomes
a) 2( p + p )
b) 2 p + p
2010
If pressure of CO2 (real gas) in a container is given by p =
ks
the gas in container is
a) 11J
RT
9
− 2 , then mass of
2V − b 4b
b) 22 J
c) 33 J
d) 44 J
A closed vessel contains 8g of oxygen and 7g of nitrogen. The total pressure is 10 atm
.s
a
4.
d) p + 2 p
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3.
c) ( p + p ) / 2
at a given temperature. If now oxygen is absorbed by introducing a suitable
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a) 2
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absorbent the pressure of the remaining gas (in atm) will be
5.
b) 10
c) 4
d) 5
Ideal gas and real gas have major difference of
a) Phase Transition
b) Temperature
c) Pressure
d) None of these above
2009
6.
By what percentage should the pressure of a given mass of a gas be increased, so as
to decrease its volume by 10% at a constant temperature?
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a) 5%
8.
c) 12.5%
d) 11.1%
When a van der Wall’s gas undergoes free expansion, then its temperature
a) Decreases
b) Increases
c) Does not change
d) Depends upon the nature of the gas
An electron tube was sealed off during manufacture at a pressure of 1.2 × 10−7 mm of
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7.
b) 7.2%
mercury at 27 0 C . Its volume is 100cm 3 . The number of molecules that remain in the
tube is
b) 3 × 1015
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9.
c) 3.89 × 1011
d) 5 × 1011
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a) 2 × 1016
At 100 C the value of the density of a fixed mass of an ideal gas divided by its pressure
is x. At 1100 C this ratio is
a) x
b)
383
x
283
c)
10
x
110
d)
283
x
383
10. A balloon contains 500m3 of He, at 27 0 C and 1 atm pressure. The volume of He, at
−30 C and 0.5 atm pressure will be
b) 900m3
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a) 700m3
c) 1000m3
d) 500m3
ks
11. The phenomenon of Brownian movement may be taken as evidence of
.s
a
a) Kinetic theory of matter
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2007
d) Photoelectric phenomenon
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c) Corpuscular theory of light
b) EMT of radiation
12. The figure below shows the plot of
pV
. Versus p for oxygen gas at two different
nT
temperatures
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Read the following statements concerning the above curves
i) The dotted line corresponds to the ‘ideal’ gas behaviour
ii) T1 > T2
pV
at the point where the curves meet on the y-axis is the same for
nT
all gases
Which of the above statements is true?
b) i and ii only
c) All of these
d) None of these
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a) i only
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iii) The value of
13. One litre of an ideal gas at 27 0 C is heated at a constant pressure to 297 0 C . Then, the
final volume is approximately
a) 1.2 L
b) 1.9L
2006
c) 19L
d) 2.4L
14. Two balloons are filled one with pure He gas and the other by air, respectively. If the
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per unit volume is
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pressure and temperature of these balloons are same then the number of molecules
.s
a
a) More in the He filled balloon
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2005
d) In the ratio of 1: 4
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c) More in air filled balloon
b) Same in both balloons
15. Real gases obey ideal gas laws more closely at
a) Low pressure and low temperature
b) Low pressure and high temperature
c) High pressure and low temperature
d) Low pressure and high temperature
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2004
16. the equation of state for 5 g of oxygen at a pressure p and temperature T, when
occupying a volume V, will be
a) pV = (5/32) RT
b) pV = 5RT
c) pV = (5/2) RT
d) pV = (5/16) RT
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17. If a given mass of gas occupies a volume of 10cc at 1atm pressure and temperature
1000 C . What will be its volume at 4 atm pressure, the temperature being the same?
a) 100 cc
b) 400 cc
c) 104 cc
d) 2.5 cc
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18. Two gases of equal masses are in thermal equilibrium. If pa , pb and Va , Vb are their
respective pressure and volumes, then which relation is true
a) 2 paVa = pbVb
b) pa ≠ pb ,Va ≠ Vb
c)
pa pb
=
Va Vb
d) paVa = pbVb
Various Speeds of Gas
2010
hi
19. The temperature of an ideal gas is increased from 120K to 480K. If at 120K, the root
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men square speed of gas molecules is v, then at 480K, it will be
b) 2v
.s
a
a) 4v
c)
v
2
d)
v
4
20. At what temperature of an ideal gas is increased from 120K to 480K. If at 120K, the
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root mean square speed of gas molecules is v, then at 480K, it will be
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a) 80K
b) -73K
c) 3K
d) 20K
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21. The speed of sound in hydrogen at NTP is 1270ms −1 . Then, the speed in a mixture of
hydrogen and oxygen in the ratio 4: 1 by volume will be
a) 317ms −1
b) 635ms −1
c) 830ms −1
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d) 950ms −1
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2006
22. Assertion (A): The root mean square and most probable speeds of the molecules in a
gas are the same.
Reason (R): The Maxwell distribution for the speed of molecules in a gas is
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symmetrical.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
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c) Assertion is true but reason is false.
d) Both assertion and reason are false.
23. The temperature of H 2 at which the rms velocity of its molecules is seven times the
rms velocity the molecules of nitrogen at 300 K is
a) 2100K
b) 1700 K
c) 1350 K
d) 1050 K
24. If at NTP velocity of sound in a gas is 1150ms −1 , then the rms velocity of gas molecules
at NTP is
b) 1532.19ms −1
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a) 1600ms −1
c) 160ms −1
d) zero
ks
25. When temperature of an ideal gas is increased from 27 0 C to 227 0 C , its rms speed is
changed from 400ms −1 to vs . The vs is
b) 450 ms −1
c) 310 ms −1
d) 746 ms −1
Pressure and Energy of Gas
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.s
a
a) 516 ms −1
2010
26. Assertion (A): If a gas container in motion is suddenly stopped, the temperature of
the gas rises.
Reason (R): The kinetic energy of ordered mechanical motion is converted into
kinetic energy of random motion of gas molecules.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
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b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false.
d) Both assertion and reason are false.
27. The kinetic energy of 1g molecule of a gas at normal temperature and pressure is (R
a) 1.3 × 102 J
b) 2.7 × 102 J
c) 0.56 × 104 J
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= 8.31 J/mol-K)
d) 3.4 × 103 J
28. Which one of the following is not an assumption in the kinetic theory of gases?
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a) The volume occupied by the molecules of the gas is negligible.
b) The force of attraction between the molecules is negligible.
c) The collision between molecules are elastic.
d) All molecules have some speed.
2009
29. A sealed container with negligible coefficient of volumetric expansion contains
a) Halved
b) Unchanged
d) Increased by factor
2
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.s
a
c) Doubled
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helium atoms is
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helium (a monoatomic gas). When it is heated from 300K to 600K, the average KE of
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30. Two vessels A and B having equal volume contain equal masses of hydrogen in A and
helium in B at 300K. Then, mark the correct statement.
a) The pressure exerted by hydrogen is half to that exerted by helium.
b) The pressure exerted by hydrogen is equal to that exerted by helium.
c) Average KE of the molecule of hydrogen is half the average KE of the molecules of
helium.
d) The pressure exerted by hydrogen is twice that exerted by helium.
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2007
31. Two cylinders fitted with pistons contain equal amounts of an ideal diatomic gas at
300K. The piston of A is free to move, while that of B is held fixed. The same amount
of heat is given to the gas in each cylinder. If the rise in temperature of gas in A is
300K, then rise in temperature of gas in B is
b) 18K
c) 50K
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d) 42K
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a) 30K
32. Pressured of an ideal gas is increased by keeping temperature constant. Kinetic
energy of molecules _____
a) Increase
b) Decrease
c) No change
d) Can’t be determined
2004
33. At which of the following temperature would the molecules of gas have twice the
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average kinetic energy they have at 200 C
b) 800 C
c) 5860 C
d) 3130 C
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a) 400 C
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a
Degrees of Freedom and Specific Heat
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34. Mean free path of gas molecule at constant temperature is inversely proportional to
a) p
b) V
c) m
d) n (number density)
2009
35. At ordinary temperature, the molecules of an ideal gas have only translational and
rotational kinetic energies. At high temperatures they may also have vibrational
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energy. As a result of this at higher temperature (CV = molar heat capacity at
constant volume)
a) CV =
3
R for a mono atomic gas
2
b) CV > R for a mono atomic gas
5
2
d) CV =
5
R for a diatomic gas
2
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c) CV < R for a diatomic gas
3
2
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2008
36. A given mass of a gas is compressed isothermally until its pressure is doubled. It is
then allowed to expand adiabatically until its original volume is restored and its
pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heat
of the gas is approximately
a) 1.20
b) 1.41
c) 1.67
d) 1.83
37. Assertion (A): Mean free path a gas molecules varies inversely as density of the gas.
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Reason (R): Mead free path varies inversely as pressure of the gas.
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a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
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a
c) Assertion is true but reason is false.
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d) Both assertion and reason are false.
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2007
38. The degrees of freedom of a molecule of a tri-atomic gas are
a) 2
b) 4
c) 6
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d) 8
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Key
2) b
3) b
4) d
5) c
6) d
7) a
8) c
9) d
10) b
11) a
12) c
13) b
14) b
15) b
16) a
17) d
18) d
19) b
20) d
21) b
22) d
23) d
24) b
25) a
26) a
27) d
28) d
29) c
30) d
31) d
32) c
33) d
34) d
35) a
36) b
37) b
38) c
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Hints
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1) d
Gas Law
1.
V ∝T
Here,
V1 T1
=
V2 T2
.s
a
T2 = 600 K
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1 300
∴ =
2 T2
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V1 = V then V2 = 2V and T1 = 300 K
T2 = 327 0 K
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So, Δt = 327 − 27
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= 3000 C
3.
⎛
μ 2a ⎞
+
p
⎜
⎟ (V − μb) = μ RT
V2 ⎠
⎝
⎛ μ RT ⎞ μ 2 a
p=⎜
⎟− 2
⎝ V − μb ⎠ V
⎞
Given equation, p = ⎛⎜
− 2⎟
⎝ 2V − b 4b ⎠
RT
a
On comparing the given equation with this standard equation, we get
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1
d
2
μ=
Hence, μ =
m
⇒ mass of gas
M
pmix = p1 + p2
=
μ1 RT
V
+
μ2 RT
V
=
m1 RT m2 RT
.
.
+
M1 V
M2 V
=
8 RT 7 RT RT
.
+ .
=
32 V
28 V
2V
10 =
RT
. ………………..(i)
2V
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4.
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1
m = μ M = × 44 = 22 g
2
7 RT
28 V
p=
RT
………….(ii)
4V
ks
p=
hi
When oxygen is absorbed then for nitrogen by pressure
.s
a
From eqs (i) and (ii) we get
Pressure of the nitrogen p = 5 atm
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pV = nRT
Or pV =
m
RT
M
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9.
Or
Or
∴
p RT
pV
1
=
RT or =
ρ M
m
M
ρ
p
=
1
T
ρ1 / p1 T2
x
383
= ⇒
=
ρ 2 / p2 T1
( ρ 2 / p2 ) 283
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Or
p2
283
x
383
=
p1V1 p2V2
=
T1
T2
∴V2 =
V2 =
co
m
p1V1T2
p2T1
Or V2 =
1× 500 × (273 − 3)
0.5 × (273 + 27)
1× 500 × 270
0.5 × 300
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10.
ρ2
V2 = 900m3
V1 T1
=
V2 T2
V1T2
T1
∴V2 = 1×
⇒ V2 =
(297 + 273)
(27 + 273)
570
300
.s
a
⇒ V2 = 1.9 L
hi
So, V2 =
ks
13.
m
5
=
molecular weight 32
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16. No. of moles n =
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pV = nRT
⇒ pV =
17.
5
RT
32
p1V1 p2V2
=
T1
T2
Here T1 = T2
And p1 = 1atm , V1 = 10cc , p2 = 4atm
Now from eq (i) p1V1 = PV
2 2
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10 ×1 = 4 × V2
V2 = 2.5cc
Various Speeds of Gas
3RT
M
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19. vrms =
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v1
T
= 1
v2
T2
So,
Now, T1 = 120 K , T2 = 480 K , v1 = v
v1
120
1 1
=
=
=
v2
480
4 2
So,
⇒
v 1
=
v2 2
⇒ v2 = 2v
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3RT
M
.s
a
T
= Constant
M
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20. C =
T 320
=
= 10
2 32
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Or
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T 273 + 47
=
2
32
Or T = 20 K
21. Density of mixture
ρm =
4V × 1 + V × 16
5V
1/2
⎛1⎞
As v ∝ ⎜ ⎟
⎝ρ⎠
∴ Velocity in mixture =
1270
= 635ms −1
1/2
(4)
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23. vrmp =
3RT
m
v1
T1 M 2
=
×
v2
M 1 T2
7=
TH × 28
2 × 300
49 =
TH × 28
600
TH =
49 × 600
= 1050 K
28
24. R =
8.3
cal g mol −1 − K −1
4.2
8.3 ⎞
⎛
CV = CP − R = ⎜ 4.8 −
⎟ = 2824
4.2 ⎠
⎝
Cv
=
4.8
= 1.69
2.824
⎛3⎞
hi
Cp
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γ=
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co
m
vH
TH M N
=
×
vN
M H TN
3
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25. vrms ∝ T
.s
a
Since, v = ⎜ ⎟vs =
× 1150 = 1532.19ms −1
1.69
γ
⎝ ⎠
vrms (1)
vrms (2)
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Hence,
∝
T1
T2
400
27 + 273
300
=
=
500
vrms (2)
227 + 273
vrms (2) = v =
500
× 400 ≈ 516 ms −1
300
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Pressure and Energy of Gas
27. E =
f
RT
2
Et rans =
3
3
RT = × 8.31× (273 + 0) = 3.4 × 103 J
2
2
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3
2
31. E = kT Or E ∝ T
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n.
E1 T1
E
273 + 20
Or 1 =
=
E2 T2
2 E1
T2
Or T2 = 2 × 293 = 586 K = 586 − 273 = 3130 C
Degrees of Freedom and Specific Heat
⇒
p2 V1
=
p1 V2
⇒
2 p V1
=
p V2
∴
V1
=2
V2
hi
1
V
ks
p∝
.s
a
36.
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pV γ = Constant
γ
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p1 ⎛ V2 ⎞
=⎜ ⎟
p2 ⎝ V1 ⎠
2p
⎛2⎞
⇒
=⎜ ⎟
0.75 p ⎝ 1 ⎠
γ
⎛8⎞
⇒ log ⎜ ⎟ = γ log 2
⎝3⎠
⇒ log 8 − log 3 = γ log 2
∴ γ = 1.41
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