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The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is:
- a)1.086 : 1
- b)1 : 1.086
- c)2 : 1.086
- d)1.086 : 2
Correct answer is 'A'. Can you explain this answer?
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Root Mean Square Velocity and Average Velocity of Gas Molecules
Root mean square velocity (urms) of a gas molecule is the square root of the sum of the squares of the velocities of all the gas molecules divided by the total number of molecules. It is given by the formula:
urms = √(3RT/M)
where R is the universal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Average velocity (uavg) of a gas molecule is the average of the velocities of all the gas molecules. It is given by the formula:
uavg = √(8RT/πM)
where π is the mathematical constant pi.
Ratio of urms to uavg
The ratio of urms to uavg is given by:
urms/uavg = √(3π/8)
This value is approximately equal to 1.086. Therefore, the correct answer is option A, which states that the ratio is 1.086 : 1.
Explanation
The ratio of urms to uavg is a constant for a given temperature and molar mass of the gas. This is because the two velocities are related to the kinetic energy of the gas molecules, which is determined by the temperature and molar mass. The root mean square velocity is proportional to the square root of the kinetic energy, while the average velocity is proportional to the square root of the average kinetic energy. The ratio of the two velocities depends only on the ratio of the two quantities, which is a constant for a given gas at a given temperature.
Therefore, the ratio of urms to uavg is a useful parameter for characterizing the properties of gas molecules. It is related to the diffusion rate, viscosity, and thermal conductivity of the gas, among other properties.
Root mean square velocity (urms) of a gas molecule is the square root of the sum of the squares of the velocities of all the gas molecules divided by the total number of molecules. It is given by the formula:
urms = √(3RT/M)
where R is the universal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Average velocity (uavg) of a gas molecule is the average of the velocities of all the gas molecules. It is given by the formula:
uavg = √(8RT/πM)
where π is the mathematical constant pi.
Ratio of urms to uavg
The ratio of urms to uavg is given by:
urms/uavg = √(3π/8)
This value is approximately equal to 1.086. Therefore, the correct answer is option A, which states that the ratio is 1.086 : 1.
Explanation
The ratio of urms to uavg is a constant for a given temperature and molar mass of the gas. This is because the two velocities are related to the kinetic energy of the gas molecules, which is determined by the temperature and molar mass. The root mean square velocity is proportional to the square root of the kinetic energy, while the average velocity is proportional to the square root of the average kinetic energy. The ratio of the two velocities depends only on the ratio of the two quantities, which is a constant for a given gas at a given temperature.
Therefore, the ratio of urms to uavg is a useful parameter for characterizing the properties of gas molecules. It is related to the diffusion rate, viscosity, and thermal conductivity of the gas, among other properties.
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The ratio of root mean square velocity to average velocity of a gas mo...
It is based on calculation, because when we derive these the final expression is comes out to be √8RT/πM : √3RT/M
On solving this, we get 1.086 : 1I hope the above content give satisfaction to you.
On solving this, we get 1.086 : 1I hope the above content give satisfaction to you.
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The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is:a)1.086 : 1b)1 : 1.086c)2 : 1.086d)1.086 : 2Correct answer is 'A'. Can you explain this answer?
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