Question:medium
The speed distribution for a sample of \(N\) gas particles is shown below. \(P(v) = 0\) for \(v > 2v_0\). How many particles have speeds between \(1.2v_0\) and \(1.8v_0\)?
![Ques Fig]()
The speed distribution for a sample of \(N\) gas particles is shown below. \(P(v) = 0\) for \(v > 2v_0\). How many particles have speeds between \(1.2v_0\) and \(1.8v_0\)?
![Ques Fig]()
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To calculate the number of particles in a specific speed range, find the area under the speed distribution curve for that range.
Updated On: Nov 28, 2025
- 0.2 N
- 0.4 N
- 0.6 N
- 0.8 N
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The Correct Option is B
Solution and Explanation
The problem defines the speed distribution function \(P(v)\), which represents particle count versus speed. The distribution \(P(v)\) is non-zero for speeds from 0 to \(2v_0\), and zero above \(2v_0\).
To find the number of particles with speeds between \(1.2v_0\) and \(1.8v_0\), we find the area under the curve in that range.
The area under the curve between \(1.2v_0\) and \(1.8v_0\) is 0.4 times the total number of particles, \(N\).
Thus, \(0.4N\) particles have speeds within this range.
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