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  4. Root mean square speed of the molecules of ideal gas is v. If pressure is increased two times at constant temperature, then the rms speed will become

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Q. Root mean square speed of the molecules of ideal gas is $v$. If pressure is increased two times at constant temperature, then the rms speed will become

AIIMSAIIMS 2012

Solution:

RMS speed of gas molecules does not depends on the pressure of gas (if temperature remains constant) because $p \propto \rho .$ If pressure is increased $n$ times density will also increase by $n$ time but $V_{ rms }$ remains constant.