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The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC is
- a)35 oC
- b)48 oC
- c)65 oC
- d)14 oC
Correct answer is option 'D'. Can you explain this answer?
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The ratio of densities of nitrogen and oxygen is 14 : 16. The temperat...
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The ratio of densities of nitrogen and oxygen is 14 : 16. The temperat...
Given Data:
- The ratio of densities of nitrogen and oxygen is 14 : 16.
- The temperature at which the speed of sound in nitrogen will be the same as that of oxygen is 55°C.
Approach:
- The speed of sound in a gas is given by the formula: v = √(γRT), where γ is the adiabatic index, R is the gas constant, and T is the temperature.
- Since the speed of sound is directly proportional to the square root of temperature, we need to find the temperature at which the speed of sound in nitrogen equals the speed of sound in oxygen.
Solution:
- Let's assume the speeds of sound in nitrogen and oxygen at 55°C are vN and vO respectively.
- Given that the ratio of densities of nitrogen and oxygen is 14 : 16, we can write: (ρN/ρO) = (16/14) = (vO/vN)^2, where ρ is the density.
- Since the densities are proportional to the molecular weights of the gases, we have: (Molecular weight of O/Molecular weight of N) = (vO/vN)^2.
- As the molecular weights of nitrogen and oxygen are 28 and 32 respectively, we get: (32/28) = (vO/vN)^2.
- Solving for vO/vN, we get vO/vN = √(32/28) = √(8/7).
- To find the temperature at which vO = vN, we need to square this ratio: (vO/vN)^2 = (8/7).
- Therefore, the temperature at which the speed of sound in nitrogen will be the same as that of oxygen is 14°C (Option D).
- The ratio of densities of nitrogen and oxygen is 14 : 16.
- The temperature at which the speed of sound in nitrogen will be the same as that of oxygen is 55°C.
Approach:
- The speed of sound in a gas is given by the formula: v = √(γRT), where γ is the adiabatic index, R is the gas constant, and T is the temperature.
- Since the speed of sound is directly proportional to the square root of temperature, we need to find the temperature at which the speed of sound in nitrogen equals the speed of sound in oxygen.
Solution:
- Let's assume the speeds of sound in nitrogen and oxygen at 55°C are vN and vO respectively.
- Given that the ratio of densities of nitrogen and oxygen is 14 : 16, we can write: (ρN/ρO) = (16/14) = (vO/vN)^2, where ρ is the density.
- Since the densities are proportional to the molecular weights of the gases, we have: (Molecular weight of O/Molecular weight of N) = (vO/vN)^2.
- As the molecular weights of nitrogen and oxygen are 28 and 32 respectively, we get: (32/28) = (vO/vN)^2.
- Solving for vO/vN, we get vO/vN = √(32/28) = √(8/7).
- To find the temperature at which vO = vN, we need to square this ratio: (vO/vN)^2 = (8/7).
- Therefore, the temperature at which the speed of sound in nitrogen will be the same as that of oxygen is 14°C (Option D).
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The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer?.
The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at 55 oC isa)35 oCb)48 oCc)65 oCd)14 oCCorrect answer is option 'D'. Can you explain this answer?.
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