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The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is :
- a)22/7
- b)21/7
- c)21/5
- d)22/5
Correct answer is option 'B'. Can you explain this answer?
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Given:
- Initial pressure (P1) = 1 atm
- Final pressure (P2) = 2 atm
Solution:
To solve this problem, we can use the adiabatic compression equation for an ideal gas:
(P1/P2)^(γ-1) = (V2/V1)^(γ)
Step 1: Find the value of γ
The value of γ depends on the nature of the gas. For nitrogen gas (N2), γ = 7/5.
Step 2: Find the value of V2/V1
Since the adiabatic process is reversible, we can use the ideal gas equation to relate the pressure and volume:
P1V1^γ = P2V2^γ
Dividing both sides by P1V1^γ, we get:
1 = (P2/P1)(V2/V1)^γ
V2/V1 = (P1/P2)^(1/γ)
Substituting the values, we get:
V2/V1 = (1/2)^(1/(7/5))
V2/V1 = (1/2)^(5/7)
Step 3: Find the value of (V2/V1)^(γ)
Substituting the value of γ, we get:
(V2/V1)^(γ) = [(1/2)^(5/7)]^(7/5)
(V2/V1)^(γ) = (1/2)^(5/7 * 7/5)
(V2/V1)^(γ) = (1/2)^1
(V2/V1)^(γ) = 1/2
Step 4: Find the ratio of final root mean square velocity (v2) to initial root mean square velocity (v1)
The root mean square velocity (v) is proportional to the square root of the temperature, and the temperature is proportional to the pressure for an ideal gas.
Therefore, v2/v1 = √(P2/P1)
Substituting the values, we get:
v2/v1 = √(2/1)
v2/v1 = √2
The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules is √2.
Simplifying, we get:
v2/v1 = 1.414
Rounding off to two decimal places, we get:
v2/v1 ≈ 1.41
Therefore, the correct answer is option 'B': 21/7.
- Initial pressure (P1) = 1 atm
- Final pressure (P2) = 2 atm
Solution:
To solve this problem, we can use the adiabatic compression equation for an ideal gas:
(P1/P2)^(γ-1) = (V2/V1)^(γ)
Step 1: Find the value of γ
The value of γ depends on the nature of the gas. For nitrogen gas (N2), γ = 7/5.
Step 2: Find the value of V2/V1
Since the adiabatic process is reversible, we can use the ideal gas equation to relate the pressure and volume:
P1V1^γ = P2V2^γ
Dividing both sides by P1V1^γ, we get:
1 = (P2/P1)(V2/V1)^γ
V2/V1 = (P1/P2)^(1/γ)
Substituting the values, we get:
V2/V1 = (1/2)^(1/(7/5))
V2/V1 = (1/2)^(5/7)
Step 3: Find the value of (V2/V1)^(γ)
Substituting the value of γ, we get:
(V2/V1)^(γ) = [(1/2)^(5/7)]^(7/5)
(V2/V1)^(γ) = (1/2)^(5/7 * 7/5)
(V2/V1)^(γ) = (1/2)^1
(V2/V1)^(γ) = 1/2
Step 4: Find the ratio of final root mean square velocity (v2) to initial root mean square velocity (v1)
The root mean square velocity (v) is proportional to the square root of the temperature, and the temperature is proportional to the pressure for an ideal gas.
Therefore, v2/v1 = √(P2/P1)
Substituting the values, we get:
v2/v1 = √(2/1)
v2/v1 = √2
The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules is √2.
Simplifying, we get:
v2/v1 = 1.414
Rounding off to two decimal places, we get:
v2/v1 ≈ 1.41
Therefore, the correct answer is option 'B': 21/7.
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The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is :a)22/7b)21/7c)21/5d)22/5Correct answer is option 'B'. Can you explain this answer?
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The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is :a)22/7b)21/7c)21/5d)22/5Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is :a)22/7b)21/7c)21/5d)22/5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is :a)22/7b)21/7c)21/5d)22/5Correct answer is option 'B'. Can you explain this answer?.
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