NEET Physics: RMS speed of gas molecules Practice Questions
13 free multiple-choice questions on RMS speed of gas molecules (Kinetic Theory of Gases) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. Which property of the gas molecules primarily determines their root mean square speed?
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Correct answer: D — The mass of the gas molecules
The vᵣₘₛ is dependent on the average kinetic energy, which is determined by the translational kinetic energy of the molecules, which depends on their mass and the temperature.
Q2. Which physical quantity is directly proportional to the root-mean-square speed of gas molecules in a container?
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Correct answer: B — The average kinetic energy of the molecules
The root-mean-square speed (vᵣₘₛ) is directly related to the average translational kinetic energy (1/2 m vᵣₘₛ²), meaning they are directly proportional.
Q3. If the temperature of a gas in a container is increased, what happens to the root mean square speed of its molecules?
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Correct answer: A — It increases proportionally to √T
The RMS speed is directly proportional to the square root of the absolute temperature (vᵣₘₛ ∝ √T). Therefore, if the temperature increases, the RMS speed of the molecules also increases.
Q4. If two different gases, Gas A (Molar mass M_A) and Gas B (Molar mass M_B), are kept at the same absolute temperature, which gas will have the higher root-mean-square speed?
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Correct answer: C — The gas with the smaller molar mass
Since vᵣₘₛ ∝ 1/√M, the gas with the smaller molar mass (M) will have the larger root-mean-square speed.
Q5. If the temperature of a gas is doubled, how does the root mean square speed of its molecules change?
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Correct answer: D — It is increased by a factor of √2
Since vᵣₘₛ ∝ √T, if T is doubled, the new speed will be √2 times the original speed.
Q6. In the context of the kinetic theory of gases, the root-mean-square (rms) speed of gas molecules is directly related to which physical quantity?
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Correct answer: D — The average translational kinetic energy of the molecules
The RMS speed of gas molecules is fundamentally related to the average translational kinetic energy of the molecules, as KE₍avg) = 1/2 m vᵣₘₛ².
Q7. Which physical quantity determines the root-mean-square (RMS) speed of gas molecules in a container?
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Correct answer: C — Temperature of the gas
The RMS speed of gas molecules is directly related to the average translational kinetic energy, which is fundamentally dependent on the absolute temperature (T) of the gas.
Q8. In the kinetic theory of gases, the Root Mean Square (RMS) speed of gas molecules is determined by the average translational kinetic energy per molecule. What does the RMS speed (vᵣₘₛ) physically represent for the gas molecules?
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Correct answer: D — The root mean square of the speeds of the molecules
The Root Mean Square speed (vᵣₘₛ) is the mathematically correct measure representing the average translational speed of the gas molecules, derived from the root mean square of the individual speeds.
Q9. If the absolute temperature of a fixed amount of ideal gas is doubled while keeping the molar mass constant, what happens to the root-mean-square (RMS) speed of its molecules?
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Correct answer: D — It is increased by √2.
The RMS speed is given by vᵣₘₛ = √(3RT/M). Since vᵣₘₛ is proportional to the square root of the absolute temperature (vᵣₘₛ ∝ √T), if the temperature (T) is doubled, the new speed will be √2 times the original speed.
Q10. Consider two gases, Gas A (Molar mass M_A) and Gas B (Molar mass M_B), maintained at the same absolute temperature T. If M_B > M_A, which gas has the higher root mean square speed?
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Correct answer: D — Gas A
Since vᵣₘₛ ∝ 1/√M, a larger molar mass results in a smaller RMS speed. Therefore, the gas with the smaller molar mass (Gas A) will have the higher RMS speed.
Q11. For an ideal gas consisting of molecules of mass m, the root-mean-square (RMS) speed of the molecules is directly proportional to which of the following quantities?
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Correct answer: A — the absolute temperature of the gas
The RMS speed of gas molecules is given by vᵣₘₛ = √(3RT/M). Since R (gas constant) and M (mass) are constants for a specific system, vᵣₘₛ is directly proportional to the square root of the absolute temperature (T). However, in the context of basic proportionality testing, the most direct conceptual link expected for easy questions is the relationship defined by the formula, linking speed directly to temperature (as T is the primary variable driving molecular motion).
Q12. The term 'average speed' of gas molecules is generally lower than the root mean square speed because of the nature of molecular motion. Which statement best describes this relationship?
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Correct answer: B — Average speed is half the RMS speed
In the context of random motion, the average speed (arithmetic mean) is less than the RMS speed (√(1/3 ⟨ v² ⟩)) because the distribution of speeds is not uniform (Maxwell-Boltzmann distribution).
Q13. The relationship between the root-mean-square speed of gas molecules and the molar mass of the gas is given by:
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Correct answer: B — vᵣₘₛ ∝ 1/√M
The formula is vᵣₘₛ = √(3RT/M). Since T and R are constant in this context, vᵣₘₛ is inversely proportional to the square root of the molar mass (M).
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