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The r.m.s. speed of the molecules of a gas in a vessel is 200 m/s. if 25% of the gas leaks out of the vessel, at constant temperature, then the r.m.s. speed of the remaining molecules will be (a) 400 m/s (b) 150 m/s (c) 100 m/s (d) 200 m/s

Shwetabh , 11 Years ago
Grade 12
anser 2 Answers
Saurabh Koranglekar

Last Activity: 4 Years ago

To solve this problem, we need to understand the relationship between the root mean square (r.m.s.) speed of gas molecules and the number of molecules present.

Step 1: Recall the r.m.s. speed formula
The r.m.s. speed of gas molecules is given by the formula:

v_rms = √(3RT/M)

Where:

v_rms = r.m.s. speed
R = universal gas constant
T = temperature (in Kelvin)
M = molar mass of the gas
Notice that the r.m.s. speed depends only on the temperature and the type of gas (molar mass). It is independent of the number of molecules.

Step 2: Effect of gas leakage
Since the problem states that 25% of the gas leaks out, the number of molecules is reduced. However, the r.m.s. speed remains unchanged because temperature remains constant.

Step 3: Conclusion
The r.m.s. speed of the remaining molecules is the same as the initial r.m.s. speed.

Answer: (d) 200 m/s

Vikas TU

Last Activity: 4 Years ago

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Dear student 
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