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A monoatomic gas is kept in a vessel at some finite temperature. Choose the correct statement(s)

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Number of atoms moving with speed equal to half of RMS speed will be more than number of atoms moving with speed equal to one third of RMS speed.

Average velocity of atoms of gas has magnitude equal to $\sqrt{\frac{8 R T}{π M}}$

Number of atoms moving with average speed will be more than number of atoms moving with RMS speed.

if its temperature (in degree Celsius) is increased to 4 times then its RMS speed will increased by a factor less than 2.

answer is A, C, D.

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Detailed Solution

$V_{r m s} = \sqrt{\frac{3 R T}{M}} w h e r e t e m p e r a t u r e T i s i n K$

$V_{m p} = \sqrt{\frac{2 R T}{M}} V_{a v g} = \sqrt{\frac{8 R T}{π M}}$

At a temperature $T^{0} C$ , $V_{r m s} = \sqrt{\frac{3 R (273 + T^{o} C)}{M}}$

$V_{r m s} = \sqrt{\frac{3 R (273 + 4 T^{o} C)}{M}} < 2 \sqrt{\frac{3 R (273 + T^{o} C)}{M}}$

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