For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

Engineering

Physics

Thermodynamics

Question

80 m/s

100 m/s

$100 \sqrt{5} m / s$

$80 \sqrt{5} m / s$

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$V_{rms} = \sqrt{\frac{3 RT}{M_{w}}}$

$\Rightarrow V_{rms} \propto \sqrt{T}$

$Now, \frac{v}{200} = \sqrt{\frac{500}{400}} \Rightarrow \frac{v}{200} = \frac{\sqrt{5}}{2}$

$\Rightarrow v = 100 \sqrt{5} m / s$