JEE Physics Kinetic Theory MCQs Set 13

Answer: (a) \( 10.35\times10^{-21} \) J

Explanation:
1. Average kinetic energy is proportional to absolute temperature.
2. T₁ = 27 + 273 = 300 K and T₂ = 227 + 273 = 500 K, so K₂/K₁ = 500/300 = 5/3.
3. \( K_2 = \tfrac{5}{3}\times 6.21\times10^{-21} = 10.35\times10^{-21} \) J.

Teacher's Note:
1. A
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138. .

Answer: (c) 375°C

Explanation:
1. \( T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1} \), so \( T_2 = T_1\left(\tfrac{V_1}{V_2}\right)^{2/3} \).
2. Since \( V_2/V_1 = 8/27 \), \( V_1/V_2=27/8 \) and \( (27/8)^{2/3}=9/4 \).
3. T₂ = 300 × 9/4 = 675 K = 402°C.
4. Rise in temperature = 402 − 27 = 375°C.

Teacher's Note:
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147. .

Answer: (c) \( 3m_A=2m_B \)

Explanation:
1. For isothermal expansion to 2V the pressure halves, so the fall in pressure is half the initial pressure: \( \Delta p=P/2 \).
2. Initial pressure \( P=\dfrac{mRT}{MV} \), hence \( \Delta p\propto m \) for the same gas, T and V.
3. \( \dfrac{\Delta p_A}{\Delta p_B}=\dfrac{m_A}{m_B}=\dfrac{1}{1.5}=\dfrac23 \), so \( 3m_A=2m_B \).

Teacher's Note:
1. A
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178. .

Answer: (c) \( \dfrac{N_1T_1+N_2T_2}{N_1+N_2} \)

Explanation:
1. No energy is lost, so total translational energy is conserved: \( \tfrac32kT_1N_1+\tfrac32kT_2N_2=\tfrac32k(N_1+N_2)T \).
2. Cancelling \( \tfrac32k \): \( T=\dfrac{N_1T_1+N_2T_2}{N_1+N_2} \).

Teacher's Note:
1. T
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108. 2
109.
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112. e
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114.
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116. ₁
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118. =
119.
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121. ₂
122. .

Answer: (d) 77°C

Explanation:
1. \( v_{rms}=\sqrt{3RT/M} \), so equal rms speeds need \( T/M \) equal.
2. For oxygen M = 32 and T = 127 + 273 = 400 K. For nitrogen M = 28.
3. \( T_{N_2}=400\times\dfrac{28}{32}=350 \) K = 77°C.

Teacher's Note:
1. E
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121. .

Answer: (c)

Explanation:
1. Heat is supplied at a constant rate, so Q = mcΔT gives a temperature rising linearly with time while the oxygen stays liquid.
2. At the boiling point (about 90 K) the temperature stays constant while the liquid vaporises (Q = mL).
3. After complete vaporisation the gas heats up linearly again.
4. This rise, flat portion, rise pattern is graph (c).

Teacher's Note:
1. T
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3. m
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186. .

Answer: (a) \( (v_{rms})_1<(v_{rms})_2<(v_{rms})_3 \) and \( (\bar K)_1=(\bar K)_2=(\bar K)_3 \)

Explanation:
1. In a mixture all gases are at the same temperature, so their average kinetic energy \( \tfrac32kT \) is equal.
2. Since \( v_{rms}\propto 1/\sqrt m \), the heaviest molecules are slowest.
3. So \( (v_{rms})_1<(v_{rms})_2<(v_{rms})_3 \) with equal average kinetic energies.

Teacher's Note:
1. E
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126. .

Answer: (c) \( \dfrac{(\gamma-1)}{2R}Mv^2\,K \)

Explanation:
1. The kinetic energy of the gas of mass m is converted into internal energy: \( \tfrac12mv^2=nC_V\Delta T \).
2. With \( n=m/M \) and \( C_V=\dfrac{R}{\gamma-1} \): \( \tfrac12mv^2=\dfrac mM\dfrac{R}{\gamma-1}\Delta T \).
3. So \( \Delta T=\dfrac{(\gamma-1)Mv^2}{2R} \) kelvin.

Teacher's Note:
1. W
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Answer: (d) 0.46 km/s

Explanation:
1. \( v_{rms}=\sqrt{3RT/M} \), so at the same temperature \( v\propto 1/\sqrt M \).
2. \( \dfrac{v_{H_2}}{v_{O_2}}=\sqrt{\dfrac{32}{2}}=4 \).
3. So \( v_{O_2}=1.84/4=0.46 \) km/s.

Teacher's Note:
1. A
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183. .

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A gas atom (monatomic) can move along x, y and z axes, so it has 3 translational degrees of freedom. The assertion is true.
2. The ratio \( C_p/C_v=\gamma \) is the definition of γ and is true.
3. The ratio γ does not explain why there are 3 degrees of freedom, so the reason is not the explanation.

Teacher's Note:
1. D
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89. d
90. i
91. a
92. t
93. o
94. m
95. i
96. c
97.
98. g
99. a
100. s
101.
102. a
103. t
104.
105. o
106. r
107. d
108. i
109. n
110. a
111. r
112. y
113.
114. t
115. e
116. m
117. p
118. e
119. r
120. a
121. t
122. u
123. r
124. e
125. .
126.
127. γ
128.
129. i
130. s
131.
132. c
133. a
134. l
135. c
136. u
137. l
138. a
139. t
140. e
141. d
142.
143. f
144. r
145. o
146. m
147.
148. t
149. h
150. e
151. m
152. ,
153.
154. n
155. o
156. t
157.
158. t
159. h
160. e
161.
162. o
163. t
164. h
165. e
166. r
167.
168. w
169. a
170. y
171.
172. r
173. o
174. u
175. n
176. d
177. .

Answer: (d) A is false, but R is true.

Explanation:
1. v_rms = √(3kT/m) and v_mp = √(2kT/m), so v_rms is about 1.22 times v_mp. The assertion is false.
2. The Maxwell speed distribution is skewed with a long tail at high speeds, not symmetrical, so the reason is false.
3. Both statements are incorrect.

Teacher's Note:
1. B
2. e
3. c
4. a
5. u
6. s
7. e
8.
9. t
10. h
11. e
12.
13. d
14. i
15. s
16. t
17. r
18. i
19. b
20. u
21. t
22. i
23. o
24. n
25.
26. i
27. s
28.
29. a
30. s
31. y
32. m
33. m
34. e
35. t
36. r
37. i
38. c
39. ,
40.
41. t
42. h
43. e
44.
45. t
46. h
47. r
48. e
49. e
50.
51. c
52. h
53. a
54. r
55. a
56. c
57. t
58. e
59. r
60. i
61. s
62. t
63. i
64. c
65.
66. s
67. p
68. e
69. e
70. d
71. s
72.
73. d
74. i
75. f
76. f
77. e
78. r
79. .
80.
81. I
82. n
83.
84. a
85.
86. s
87. y
88. m
89. m
90. e
91. t
92. r
93. i
94. c
95.
96. d
97. i
98. s
99. t
100. r
101. i
102. b
103. u
104. t
105. i
106. o
107. n
108.
109. m
110. e
111. a
112. n
113. ,
114.
115. m
116. o
117. d
118. e
119.
120. a
121. n
122. d
123.
124. r
125. m
126. s
127.
128. w
129. o
130. u
131. l
132. d
133.
134. c
135. o
136. i
137. n
138. c
139. i
140. d
141. e
142. .

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. \( \gamma=1+\dfrac2f \).
2. Monatomic: f = 3, so γ = 5/3 = 1.67. Diatomic: f = 5, so γ = 7/5 = 1.4.
3. Thus γ(diatomic) < γ(monatomic) because the diatomic molecule has more degrees of freedom. Both are true and the reason explains the assertion.

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. m
26. e
27. a
28. n
29. s
30.
31. a
32.
33. s
34. m
35. a
36. l
37. l
38. e
39. r
40.
41. γ
42. .
43.
44. T
45. h
46. i
47. s
48.
49. i
50. s
51.
52. w
53. h
54. y
55.
56. γ
57.
58. i
59. s
60.
61. 1
62. .
63. 6
64. 7
65. ,
66.
67. 1
68. .
69. 4
70.
71. a
72. n
73. d
74.
75. 1
76. .
77. 3
78. 3
79.
80. f
81. o
82. r
83.
84. m
85. o
86. n
87. a
88. t
89. o
90. m
91. i
92. c
93. ,
94.
95. d
96. i
97. a
98. t
99. o
100. m
101. i
102. c
103.
104. a
105. n
106. d
107.
108. n
109. o
110. n
111. -
112. l
113. i
114. n
115. e
116. a
117. r
118.
119. p
120. o
121. l
122. y
123. a
124. t
125. o
126. m
127. i
128. c
129.
130. g
131. a
132. s
133. e
134. s
135. .

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Total translational kinetic energy is \( \tfrac32nRT=\tfrac32PV \), so the assertion is true.
2. Molecules do collide and exchange velocities, so the reason is also true.
3. The collisions do not lead to the 3/2 factor, so the reason is not the explanation.

Teacher's Note:
1. F
2. r
3. o
4. m
5.
6. k
7. i
8. n
9. e
10. t
11. i
12. c
13.
14. t
15. h
16. e
17. o
18. r
19. y
20. ,
21.
22. P
23. V
24.
25. =
26.
27. (
28. 1
29. /
30. 3
31. )
32.
33. N
34.
35. m
36.
37. v
38. _
39. r
40. m
41. s
42. ²
43. ,
44.
45. w
46. h
47. i
48. c
49. h
50.
51. g
52. i
53. v
54. e
55. s
56.
57. t
58. o
59. t
60. a
61. l
62.
63. t
64. r
65. a
66. n
67. s
68. l
69. a
70. t
71. i
72. o
73. n
74. a
75. l
76.
77. K
78. E
79.
80. =
81.
82. (
83. 3
84. /
85. 2
86. )
87. P
88. V
89. .
90.
91. C
92. o
93. l
94. l
95. i
96. s
97. i
98. o
99. n
100. s
101.
102. o
103. n
104. l
105. y
106.
107. r
108. e
109. d
110. i
111. s
112. t
113. r
114. i
115. b
116. u
117. t
118. e
119.
120. e
121. n
122. e
123. r
124. g
125. y
126.
127. a
128. m
129. o
130. n
131. g
132.
133. m
134. o
135. l
136. e
137. c
138. u
139. l
140. e
141. s
142. .

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The mean free path is \( \lambda=\dfrac{kT}{\sqrt2\pi\sigma^2P}=\dfrac{1}{\sqrt2\pi\sigma^2 n} \), so it varies inversely as the number density and hence as the density. The assertion is true.
2. At constant temperature the density is proportional to the pressure, so λ varies inversely as the pressure too. The reason is true.
3. The pressure dependence is the reason the density dependence holds, so the reason explains the assertion.

Teacher's Note:
1. M
2. e
3. a
4. n
5.
6. f
7. r
8. e
9. e
10.
11. p
12. a
13. t
14. h
15.
16. i
17. n
18. c
19. r
20. e
21. a
22. s
23. e
24. s
25.
26. w
27. i
28. t
29. h
30.
31. t
32. e
33. m
34. p
35. e
36. r
37. a
38. t
39. u
40. r
41. e
42.
43. a
44. n
45. d
46.
47. f
48. a
49. l
50. l
51. s
52.
53. w
54. i
55. t
56. h
57.
58. p
59. r
60. e
61. s
62. s
63. u
64. r
65. e
66.
67. a
68. n
69. d
70.
71. m
72. o
73. l
74. e
75. c
76. u
77. l
78. a
79. r
80.
81. d
82. i
83. a
84. m
85. e
86. t
87. e
88. r
89. .
90.
91. A
92. t
93.
94. l
95. o
96. w
97. e
98. r
99.
100. p
101. r
102. e
103. s
104. s
105. u
106. r
107. e
108.
109. m
110. o
111. l
112. e
113. c
114. u
115. l
116. e
117. s
118.
119. t
120. r
121. a
122. v
123. e
124. l
125.
126. f
127. a
128. r
129. t
130. h
131. e
132. r
133.
134. b
135. e
136. t
137. w
138. e
139. e
140. n
141.
142. c
143. o
144. l
145. l
146. i
147. s
148. i
149. o
150. n
151. s
152. .

Answer: (d) A is false, but R is true.

Explanation:
1. For any gas \( C_p-C_v=R>0 \), so the specific heat at constant pressure is greater. The assertion is false.
2. At constant pressure extra heat is needed to do work of expansion, not at constant volume. The reason is false.
3. Both statements are incorrect.

Teacher's Note:
1. C
2. p
3.
4. i
5. s
6.
7. a
8. l
9. w
10. a
11. y
12. s
13.
14. l
15. a
16. r
17. g
18. e
19. r
20.
21. t
22. h
23. a
24. n
25.
26. C
27. v
28.
29. b
30. e
31. c
32. a
33. u
34. s
35. e
36.
37. a
38. t
39.
40. c
41. o
42. n
43. s
44. t
45. a
46. n
47. t
48.
49. p
50. r
51. e
52. s
53. s
54. u
55. r
56. e
57.
58. p
59. a
60. r
61. t
62.
63. o
64. f
65.
66. t
67. h
68. e
69.
70. h
71. e
72. a
73. t
74.
75. g
76. o
77. e
78. s
79.
80. i
81. n
82. t
83. o
84.
85. e
86. x
87. p
88. a
89. n
90. s
91. i
92. o
93. n
94.
95. w
96. o
97. r
98. k
99. .
100.
101. T
102. h
103. e
104.
105. r
106. e
107. l
108. a
109. t
110. i
111. o
112. n
113.
114. i
115. s
116.
117. M
118. a
119. y
120. e
121. r
122. '
123. s
124.
125. r
126. e
127. l
128. a
129. t
130. i
131. o
132. n
133.
134. C
135. p
136.
137. −
138.
139. C
140. v
141.
142. =
143.
144. R
145. .

Answer: (c) A is true, but R is false.

Explanation:
1. A mole always contains Avogadro's number of particles, 6.02×10²³, whatever the temperature or volume. The assertion is true.
2. Only the molar volume of a gas (22.4 L) refers to STP; a mole does not, so the reason is false.

Teacher's Note:
1. T
2. h
3. e
4.
5. m
6. o
7. l
8. e
9.
10. i
11. s
12.
13. a
14.
15. c
16. o
17. u
18. n
19. t
20.
21. o
22. f
23.
24. p
25. a
26. r
27. t
28. i
29. c
30. l
31. e
32. s
33.
34. a
35. n
36. d
37.
38. i
39. s
40.
41. i
42. n
43. d
44. e
45. p
46. e
47. n
48. d
49. e
50. n
51. t
52.
53. o
54. f
55.
56. c
57. o
58. n
59. d
60. i
61. t
62. i
63. o
64. n
65. s
66. .
67.
68. O
69. n
70. l
71. y
72.
73. t
74. h
75. e
76.
77. v
78. o
79. l
80. u
81. m
82. e
83.
84. o
85. c
86. c
87. u
88. p
89. i
90. e
91. d
92.
93. b
94. y
95.
96. a
97.
98. m
99. o
100. l
101. e
102.
103. o
104. f
105.
106. g
107. a
108. s
109.
110. d
111. e
112. p
113. e
114. n
115. d
116. s
117.
118. o
119. n
120.
121. t
122. e
123. m
124. p
125. e
126. r
127. a
128. t
129. u
130. r
131. e
132.
133. a
134. n
135. d
136.
137. p
138. r
139. e
140. s
141. s
142. u
143. r
144. e
145. .

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. During driving the tyre air warms because of flexing and friction, and at nearly constant volume \( P\propto T \), so the pressure rises. The assertion is true.
2. Even at absolute zero, particles retain zero-point energy, so the reason is true.
3. The reason has no bearing on the pressure rise, so it is not the explanation.

Teacher's Note:
1. G
2. a
3. y
4. -
5. L
6. u
7. s
8. s
9. a
10. c
11. '
12. s
13.
14. l
15. a
16. w
17.
18. s
19. a
20. y
21. s
22.
23. p
24. r
25. e
26. s
27. s
28. u
29. r
30. e
31.
32. i
33. s
34.
35. p
36. r
37. o
38. p
39. o
40. r
41. t
42. i
43. o
44. n
45. a
46. l
47.
48. t
49. o
50.
51. a
52. b
53. s
54. o
55. l
56. u
57. t
58. e
59.
60. t
61. e
62. m
63. p
64. e
65. r
66. a
67. t
68. u
69. r
70. e
71.
72. a
73. t
74.
75. c
76. o
77. n
78. s
79. t
80. a
81. n
82. t
83.
84. v
85. o
86. l
87. u
88. m
89. e
90. .
91.
92. T
93. h
94. a
95. t
96.
97. i
98. s
99.
100. w
101. h
102. y
103.
104. t
105. y
106. r
107. e
108.
109. p
110. r
111. e
112. s
113. s
114. u
115. r
116. e
117.
118. s
119. h
120. o
121. u
122. l
123. d
124.
125. b
126. e
127.
128. c
129. h
130. e
131. c
132. k
133. e
134. d
135.
136. w
137. h
138. e
139. n
140.
141. t
142. h
143. e
144.
145. t
146. y
147. r
148. e
149. s
150.
151. a
152. r
153. e
154.
155. c
156. o
157. l
158. d
159. .