JEE Physics Kinetic Theory MCQs Set 14

Answer: (a) the kinetic theory of matter (continuous random motion of molecules)

Explanation:
1. Small suspended particles zigzag because they are struck unevenly by the rapidly moving molecules of the fluid.
2. This is direct evidence that molecules are in ceaseless random motion, the basis of kinetic theory.

Teacher's Note:
1. B
2. r
3. o
4. w
5. n
6. i
7. a
8. n
9.
10. m
11. o
12. t
13. i
14. o
15. n
16.
17. m
18. a
19. k
20. e
21. s
22.
23. t
24. h
25. e
26.
27. m
28. o
29. l
30. e
31. c
32. u
33. l
34. a
35. r
36.
37. m
38. o
39. t
40. i
41. o
42. n
43.
44. v
45. i
46. s
47. i
48. b
49. l
50. e
51.
52. i
53. n
54. d
55. i
56. r
57. e
58. c
59. t
60. l
61. y
62. .

Answer: (a) Boyle's law

Explanation:
1. \( P \propto 1/V \) at constant temperature is Boyle's law, \( PV = \) constant.

Teacher's Note:
1. C
2. h
3. a
4. r
5. l
6. e
7. s
8. '
9.
10. l
11. a
12. w
13.
14. c
15. o
16. n
17. n
18. e
19. c
20. t
21. s
22.
23. V
24.
25. a
26. n
27. d
28.
29. T
30.
31. a
32. t
33.
34. c
35. o
36. n
37. s
38. t
39. a
40. n
41. t
42.
43. P
44. .
45.
46. G
47. a
48. y
49. -
50. L
51. u
52. s
53. s
54. a
55. c
56. '
57. s
58.
59. l
60. a
61. w
62.
63. c
64. o
65. n
66. n
67. e
68. c
69. t
70. s
71.
72. P
73.
74. a
75. n
76. d
77.
78. T
79.
80. a
81. t
82.
83. c
84. o
85. n
86. s
87. t
88. a
89. n
90. t
91.
92. V
93. .

Answer: (a) \( \dfrac{3}{2}k_BT \)

Explanation:
1. The translational kinetic energy per molecule is \( \dfrac{1}{2}m\overline{v^2} = \dfrac{3}{2}k_BT \).
2. It depends only on temperature, not on the nature of the gas.

Teacher's Note:
1. A
2. t
3.
4. t
5. h
6. e
7.
8. s
9. a
10. m
11. e
12.
13. t
14. e
15. m
16. p
17. e
18. r
19. a
20. t
21. u
22. r
23. e
24.
25. a
26. l
27. l
28.
29. i
30. d
31. e
32. a
33. l
34.
35. g
36. a
37. s
38.
39. m
40. o
41. l
42. e
43. c
44. u
45. l
46. e
47. s
48.
49. h
50. a
51. v
52. e
53.
54. t
55. h
56. e
57.
58. s
59. a
60. m
61. e
62.
63. a
64. v
65. e
66. r
67. a
68. g
69. e
70.
71. t
72. r
73. a
74. n
75. s
76. l
77. a
78. t
79. i
80. o
81. n
82. a
83. l
84.
85. k
86. i
87. n
88. e
89. t
90. i
91. c
92.
93. e
94. n
95. e
96. r
97. g
98. y
99. .

Answer: (a) perfectly elastic

Explanation:
1. There is no loss of kinetic energy in collisions between molecules, so the collisions are perfectly elastic.

Teacher's Note:
1. E
2. l
3. a
4. s
5. t
6. i
7. c
8.
9. c
10. o
11. l
12. l
13. i
14. s
15. i
16. o
17. n
18. s
19.
20. k
21. e
22. e
23. p
24.
25. t
26. h
27. e
28.
29. t
30. o
31. t
32. a
33. l
34.
35. k
36. i
37. n
38. e
39. t
40. i
41. c
42.
43. e
44. n
45. e
46. r
47. g
48. y
49.
50. o
51. f
52.
53. t
54. h
55. e
56.
57. g
58. a
59. s
60.
61. c
62. o
63. n
64. s
65. t
66. a
67. n
68. t
69. .

Answer: (a) \( \dfrac{5}{3} \)

Explanation:
1. For a monoatomic gas \( C_V = \dfrac{3}{2}R \) and \( C_P = C_V + R = \dfrac{5}{2}R \).
2. \( \gamma = \dfrac{C_P}{C_V} = \dfrac{5}{3} \).

Teacher's Note:
1. U
2. s
3. e
4.
5. \
6. (
7.
8. \
9. g
10. a
11. m
12. m
13. a
14.
15. =
16.
17. 1
18.
19. +
20.
21. 2
22. /
23. f
24.
25. \
26. )
27.
28. w
29. i
30. t
31. h
32.
33. f
34.
35. =
36.
37. 3
38.
39. f
40. o
41. r
42.
43. m
44. o
45. n
46. o
47. a
48. t
49. o
50. m
51. i
52. c
53.
54. g
55. a
56. s
57. e
58. s
59. .

Answer: (a) 3

Explanation:
1. The fly is free to move anywhere in space, which needs three coordinates, so it has three translational degrees of freedom.

Teacher's Note:
1. A
2.
3. f
4. r
5. e
6. e
7.
8. p
9. a
10. r
11. t
12. i
13. c
14. l
15. e
16.
17. i
18. n
19.
20. s
21. p
22. a
23. c
24. e
25.
26. h
27. a
28. s
29.
30. t
31. h
32. r
33. e
34. e
35.
36. d
37. e
38. g
39. r
40. e
41. e
42. s
43.
44. o
45. f
46.
47. f
48. r
49. e
50. e
51. d
52. o
53. m
54. .

Answer: (a) increases

Explanation:
1. \( \lambda = \dfrac{k_BT}{\sqrt{2}\pi d^2P} \) at fixed temperature, so lower pressure gives a longer mean free path.

Teacher's Note:
1. F
2. e
3. w
4. e
5. r
6.
7. m
8. o
9. l
10. e
11. c
12. u
13. l
14. e
15. s
16.
17. p
18. e
19. r
20.
21. u
22. n
23. i
24. t
25.
26. v
27. o
28. l
29. u
30. m
31. e
32.
33. m
34. e
35. a
36. n
37.
38. l
39. o
40. n
41. g
42. e
43. r
44.
45. t
46. r
47. a
48. v
49. e
50. l
51.
52. b
53. e
54. t
55. w
56. e
57. e
58. n
59.
60. c
61. o
62. l
63. l
64. i
65. s
66. i
67. o
68. n
69. s
70. .

Answer: (b) The mean free path of gas molecules is \( \lambda = \dfrac{k_BT}{\sqrt{2}\pi d^2p} \)

Explanation:
1. Average translational kinetic energy is \( \dfrac{3}{2}k_BT \), not \( 3k_BT \).
2. \( C_P - C_V = R \) holds for every ideal gas.
3. Collisions with the walls transfer momentum, which gives pressure.
4. The mean free path expression in (b) is correct.

Teacher's Note:
1. C
2. h
3. e
4. c
5. k
6.
7. e
8. a
9. c
10. h
11.
12. f
13. o
14. r
15. m
16. u
17. l
18. a
19. .
20.
21. T
22. h
23. e
24.
25. m
26. e
27. a
28. n
29.
30. f
31. r
32. e
33. e
34.
35. p
36. a
37. t
38. h
39.
40. e
41. x
42. p
43. r
44. e
45. s
46. s
47. i
48. o
49. n
50.
51. i
52. s
53.
54. a
55.
56. s
57. t
58. a
59. n
60. d
61. a
62. r
63. d
64.
65. r
66. e
67. s
68. u
69. l
70. t
71. .

Answer: (a) transfer momentum to the walls

Explanation:
1. Each elastic collision reverses the normal component of momentum, so momentum \( 2mv_x \) is transferred to the wall.
2. The sum of these transfers gives the gas pressure.

Teacher's Note:
1. P
2. r
3. e
4. s
5. s
6. u
7. r
8. e
9.
10. i
11. s
12.
13. t
14. h
15. e
16.
17. a
18. v
19. e
20. r
21. a
22. g
23. e
24.
25. f
26. o
27. r
28. c
29. e
30.
31. p
32. e
33. r
34.
35. u
36. n
37. i
38. t
39.
40. a
41. r
42. e
43. a
44.
45. f
46. r
47. o
48. m
49.
50. m
51. o
52. l
53. e
54. c
55. u
56. l
57. a
58. r
59.
60. i
61. m
62. p
63. a
64. c
65. t
66. s
67. .

Answer: (a) There is a distribution of molecular speeds in a gas

Explanation:
1. Collisions keep exchanging energy, so molecules have a range of speeds given by the Maxwell distribution.
2. Average translational kinetic energy depends only on temperature, and \( v_{rms} \) depends on molar mass.

Teacher's Note:
1. A
2.
3. g
4. a
5. s
6.
7. h
8. a
9. s
10.
11. a
12.
13. s
14. p
15. r
16. e
17. a
18. d
19.
20. o
21. f
22.
23. s
24. p
25. e
26. e
27. d
28. s
29. ,
30.
31. n
32. o
33. t
34.
35. a
36.
37. s
38. i
39. n
40. g
41. l
42. e
43.
44. s
45. p
46. e
47. e
48. d
49. .

Answer: (d) all of the above

Explanation:
1. Kinetic theory models an ideal gas, studies molecular motion and relates temperature to average kinetic energy.

Teacher's Note:
1. K
2. i
3. n
4. e
5. t
6. i
7. c
8.
9. t
10. h
11. e
12. o
13. r
14. y
15.
16. l
17. i
18. n
19. k
20. s
21.
22. m
23. i
24. c
25. r
26. o
27. s
28. c
29. o
30. p
31. i
32. c
33.
34. m
35. o
36. t
37. i
38. o
39. n
40.
41. w
42. i
43. t
44. h
45.
46. m
47. a
48. c
49. r
50. o
51. s
52. c
53. o
54. p
55. i
56. c
57.
58. p
59. r
60. o
61. p
62. e
63. r
64. t
65. i
66. e
67. s
68.
69. s
70. u
71. c
72. h
73.
74. a
75. s
76.
77. p
78. r
79. e
80. s
81. s
82. u
83. r
84. e
85.
86. a
87. n
88. d
89.
90. t
91. e
92. m
93. p
94. e
95. r
96. a
97. t
98. u
99. r
100. e
101. .

Answer: (b) a monoatomic gas

Explanation:
1. \( \gamma = 1 + \dfrac{2}{f} \), where f is the number of degrees of freedom.
2. f is smallest (3) for a monoatomic gas, so \( \gamma \) is largest (5/3).

Teacher's Note:
1. M
2. o
3. r
4. e
5.
6. d
7. e
8. g
9. r
10. e
11. e
12. s
13.
14. o
15. f
16.
17. f
18. r
19. e
20. e
21. d
22. o
23. m
24.
25. g
26. i
27. v
28. e
29.
30. a
31.
32. s
33. m
34. a
35. l
36. l
37. e
38. r
39.
40. v
41. a
42. l
43. u
44. e
45.
46. o
47. f
48.
49. \
50. (
51.
52. \
53. g
54. a
55. m
56. m
57. a
58.
59. \
60. )
61. .

Answer: (b) in thermal equilibrium the energy of a gas is shared equally among all its degrees of freedom, so it has equal energies in the x, y and z directions

Explanation:
1. The law says that each degree of freedom gets \( \dfrac{1}{2}k_BT \) per molecule in thermal equilibrium.
2. So the three translational directions have equal energy.

Teacher's Note:
1. E
2. q
3. u
4. i
5. p
6. a
7. r
8. t
9. i
10. t
11. i
12. o
13. n
14.
15. i
16. s
17.
18. p
19. e
20. r
21.
22. d
23. e
24. g
25. r
26. e
27. e
28.
29. o
30. f
31.
32. f
33. r
34. e
35. e
36. d
37. o
38. m
39. ,
40.
41. n
42. o
43. t
44.
45. p
46. e
47. r
48.
49. m
50. o
51. l
52. e
53. c
54. u
55. l
56. e
57.
58. o
59. r
60.
61. p
62. e
63. r
64.
65. e
66. n
67. e
68. r
69. g
70. y
71.
72. t
73. y
74. p
75. e
76. .

Answer: (d) the total kinetic energy of the gas molecules

Explanation:
1. There is no interaction between ideal gas molecules, so the potential energy is zero.
2. The internal energy is therefore the total kinetic energy of the molecules (translational, rotational and vibrational).

Teacher's Note:
1. I
2. n
3. t
4. e
5. r
6. n
7. a
8. l
9.
10. e
11. n
12. e
13. r
14. g
15. y
16.
17. o
18. f
19.
20. a
21. n
22.
23. i
24. d
25. e
26. a
27. l
28.
29. g
30. a
31. s
32.
33. i
34. s
35.
36. a
37.
38. f
39. u
40. n
41. c
42. t
43. i
44. o
45. n
46.
47. o
48. f
49.
50. t
51. e
52. m
53. p
54. e
55. r
56. a
57. t
58. u
59. r
60. e
61.
62. o
63. n
64. l
65. y
66. .

Answer: (c) 5

Explanation:
1. CO\( _2 \) is a linear molecule.
2. It has 3 translational and 2 rotational degrees of freedom, so f = 5 (vibrations are not excited at ordinary temperatures).

Teacher's Note:
1. A
2.
3. l
4. i
5. n
6. e
7. a
8. r
9.
10. m
11. o
12. l
13. e
14. c
15. u
16. l
17. e
18.
19. h
20. a
21. s
22.
23. o
24. n
25. l
26. y
27.
28. t
29. w
30. o
31.
32. r
33. o
34. t
35. a
36. t
37. i
38. o
39. n
40. a
41. l
42.
43. d
44. e
45. g
46. r
47. e
48. e
49. s
50.
51. o
52. f
53.
54. f
55. r
56. e
57. e
58. d
59. o
60. m
61. .

Answer: (c) \( C_s = C\sqrt{\gamma/3} \)

Explanation:
1. \( C_s = \sqrt{\dfrac{\gamma P}{\rho}} \) and \( C = \sqrt{\dfrac{3P}{\rho}} \).
2. \( \dfrac{C_s}{C} = \sqrt{\dfrac{\gamma}{3}} \).

Teacher's Note:
1. S
2. i
3. n
4. c
5. e
6.
7. \
8. (
9.
10. \
11. g
12. a
13. m
14. m
15. a
16.
17. <
18.
19. 3
20.
21. \
22. )
23. ,
24.
25. t
26. h
27. e
28.
29. s
30. p
31. e
32. e
33. d
34.
35. o
36. f
37.
38. s
39. o
40. u
41. n
42. d
43.
44. i
45. s
46.
47. l
48. e
49. s
50. s
51.
52. t
53. h
54. a
55. n
56.
57. t
58. h
59. e
60.
61. r
62. m
63. s
64.
65. s
66. p
67. e
68. e
69. d
70. .
71.
72. O
73. p
74. t
75. i
76. o
77. n
78.
79. (
80. a
81. )
82.
83. i
84. s
85.
86. a
87.
88. c
89. o
90. n
91. s
92. e
93. q
94. u
95. e
96. n
97. c
98. e
99. ,
100.
101. b
102. u
103. t
104.
105. (
106. c
107. )
108.
109. i
110. s
111.
112. t
113. h
114. e
115.
116. e
117. x
118. a
119. c
120. t
121.
122. r
123. e
124. l
125. a
126. t
127. i
128. o
129. n
130. .

Answer: (d) gets doubled

Explanation:
1. \( v_{rms} \propto \sqrt{T} \). The temperature changes from 300 K to 1200 K.
2. The temperature is four times larger, so the speed doubles.

Teacher's Note:
1. A
2. l
3. w
4. a
5. y
6. s
7.
8. c
9. o
10. n
11. v
12. e
13. r
14. t
15.
16. C
17. e
18. l
19. s
20. i
21. u
22. s
23.
24. t
25. o
26.
27. k
28. e
29. l
30. v
31. i
32. n
33.
34. b
35. e
36. f
37. o
38. r
39. e
40.
41. c
42. o
43. m
44. p
45. a
46. r
47. i
48. n
49. g
50.
51. t
52. e
53. m
54. p
55. e
56. r
57. a
58. t
59. u
60. r
61. e
62. s
63. .

Answer: (b) \( C_P = 3R \)

Explanation:
1. \( C_V = \dfrac{R}{\gamma-1} = \dfrac{R}{0.5} = 2R \).
2. \( C_P = \gamma C_V = 1.5\times2R = 3R \).

Teacher's Note:
1. U
2. s
3. e
4.
5. \
6. (
7.
8. C
9. _
10. V
11.
12. =
13.
14. R
15. /
16. (
17. \
18. g
19. a
20. m
21. m
22. a
23. -
24. 1
25. )
26.
27. \
28. )
29.
30. a
31. n
32. d
33.
34. \
35. (
36.
37. C
38. _
39. P
40.
41. =
42.
43. \
44. g
45. a
46. m
47. m
48. a
49.
50. R
51. /
52. (
53. \
54. g
55. a
56. m
57. m
58. a
59. -
60. 1
61. )
62.
63. \
64. )
65. .

Answer: (d) all of these

Explanation:
1. \( C_V = \dfrac{f}{2}R \) from equipartition.
2. \( \gamma = 1 + \dfrac{2}{f} \), so \( C_V = \dfrac{R}{\gamma-1} \).
3. \( \gamma = C_P/C_V \) gives \( C_V = C_P/\gamma \). All three are correct.

Teacher's Note:
1. A
2. l
3. l
4.
5. t
6. h
7. r
8. e
9. e
10.
11. f
12. o
13. r
14. m
15. s
16.
17. a
18. r
19. e
20.
21. u
22. s
23. e
24. d
25.
26. i
27. n
28. t
29. e
30. r
31. c
32. h
33. a
34. n
35. g
36. e
37. a
38. b
39. l
40. y
41.
42. i
43. n
44.
45. p
46. r
47. o
48. b
49. l
50. e
51. m
52. s
53. .

Answer: (d) have the same mass but negligible volume

Explanation:
1. The molecules of a given gas are identical (same mass) and their size is negligible compared with the volume of the container.

Teacher's Note:
1. T
2. h
3. e
4.
5. p
6. o
7. i
8. n
9. t
10. -
11. m
12. a
13. s
14. s
15.
16. a
17. s
18. s
19. u
20. m
21. p
22. t
23. i
24. o
25. n
26.
27. i
28. s
29.
30. w
31. h
32. y
33.
34. t
35. h
36. e
37.
38. m
39. o
40. d
41. e
42. l
43.
44. w
45. o
46. r
47. k
48. s
49.
50. w
51. e
52. l
53. l
54.
55. a
56. t
57.
58. l
59. o
60. w
61.
62. p
63. r
64. e
65. s
66. s
67. u
68. r
69. e
70. .