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From the concept of kinetic theory, mean travel velocity of the gas molecules is prescribed by the relation
Where,
G = Universal gas constant
M = Molecular weight of the gas
T = Absolute temperature
G = Universal gas constant
M = Molecular weight of the gas
T = Absolute temperature
- a)V = (3M/GT) 1/2
- b)V = (3GT/M) 1/2
- c)V = (6T/GM) 1/2
- d)V = (3GT/2M) 1/2
Correct answer is option 'B'. Can you explain this answer?
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From the concept of kinetic theory, mean travel velocity of the gas mo...
Heat transfer by conduction in gases occurs through transport of the kinetic energy of molecular motion resulting from the random movement and collisions of the molecules.
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From the concept of kinetic theory, mean travel velocity of the gas mo...
Mean travel velocity of gas molecules is prescribed by the relation:
V = (3GT/M)^(1/2)
Explanation:
1. Kinetic Theory of Gases:
The kinetic theory of gases describes the behavior of gas molecules based on their motion and collisions.
According to the kinetic theory, gas molecules are in constant random motion and collide with each other and the walls of the container.
2. Mean Travel Velocity:
The mean travel velocity of gas molecules refers to the average velocity at which the gas molecules move.
It is calculated by taking into account the individual velocities of all the gas molecules in a sample and averaging them.
3. Relation between Mean Travel Velocity and Other Variables:
The mean travel velocity of gas molecules is related to the universal gas constant (G), the molecular weight of the gas (M), and the absolute temperature (T).
4. Deriving the Relation:
To derive the relation, we start with the kinetic energy of a gas molecule, which is given by the equation:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass of the gas molecule, and v is its velocity.
5. Average Kinetic Energy:
The average kinetic energy of the gas molecules is related to the temperature of the gas. According to the kinetic theory, the average kinetic energy is directly proportional to the absolute temperature:
KE = (3/2)kT
where k is the Boltzmann constant.
6. Equating the Equations:
By equating the two equations for kinetic energy, we get:
(1/2)mv^2 = (3/2)kT
Simplifying the equation:
v^2 = (3kT)/m
7. Substituting the Constants:
The Boltzmann constant (k) can be expressed in terms of the universal gas constant (R) as follows:
k = R/N
where N is Avogadro's number.
Substituting this into the equation and rearranging:
v^2 = (3RT)/(Nm)
8. Molecular Weight and Gas Constant:
The molecular weight of a gas (M) is equal to the mass of one mole of the gas molecules (m) divided by Avogadro's number (N).
M = m/N
Substituting this into the equation:
v^2 = (3RT)/(MN)
Taking the square root of both sides:
v = (3RT/M)^(1/2)
9. Final Relation:
The final relation for the mean travel velocity of gas molecules is:
V = (3GT/M)^(1/2)
where G is the universal gas constant and T is the absolute temperature.
Therefore, the correct answer is option 'B': V = (3GT/M)^(1/2).
V = (3GT/M)^(1/2)
Explanation:
1. Kinetic Theory of Gases:
The kinetic theory of gases describes the behavior of gas molecules based on their motion and collisions.
According to the kinetic theory, gas molecules are in constant random motion and collide with each other and the walls of the container.
2. Mean Travel Velocity:
The mean travel velocity of gas molecules refers to the average velocity at which the gas molecules move.
It is calculated by taking into account the individual velocities of all the gas molecules in a sample and averaging them.
3. Relation between Mean Travel Velocity and Other Variables:
The mean travel velocity of gas molecules is related to the universal gas constant (G), the molecular weight of the gas (M), and the absolute temperature (T).
4. Deriving the Relation:
To derive the relation, we start with the kinetic energy of a gas molecule, which is given by the equation:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass of the gas molecule, and v is its velocity.
5. Average Kinetic Energy:
The average kinetic energy of the gas molecules is related to the temperature of the gas. According to the kinetic theory, the average kinetic energy is directly proportional to the absolute temperature:
KE = (3/2)kT
where k is the Boltzmann constant.
6. Equating the Equations:
By equating the two equations for kinetic energy, we get:
(1/2)mv^2 = (3/2)kT
Simplifying the equation:
v^2 = (3kT)/m
7. Substituting the Constants:
The Boltzmann constant (k) can be expressed in terms of the universal gas constant (R) as follows:
k = R/N
where N is Avogadro's number.
Substituting this into the equation and rearranging:
v^2 = (3RT)/(Nm)
8. Molecular Weight and Gas Constant:
The molecular weight of a gas (M) is equal to the mass of one mole of the gas molecules (m) divided by Avogadro's number (N).
M = m/N
Substituting this into the equation:
v^2 = (3RT)/(MN)
Taking the square root of both sides:
v = (3RT/M)^(1/2)
9. Final Relation:
The final relation for the mean travel velocity of gas molecules is:
V = (3GT/M)^(1/2)
where G is the universal gas constant and T is the absolute temperature.
Therefore, the correct answer is option 'B': V = (3GT/M)^(1/2).
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From the concept of kinetic theory, mean travel velocity of the gas molecules is prescribed by the relationWhere,G = Universal gas constantM = Molecular weight of the gasT = Absolute temperaturea)V = (3M/GT)1/2b)V = (3GT/M)1/2c)V = (6T/GM)1/2d)V = (3GT/2M)1/2Correct answer is option 'B'. Can you explain this answer?
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