A) \[{{d}^{2}}\]
B) d
C) \[\sqrt{d}\]
D) \[1/\sqrt{d}\]
Correct Answer: D
Solution :
\[{{U}_{rms}}\,=\sqrt{\frac{3RT}{M}}\] using ideal gas equation, \[PV=nRT=\frac{w}{M}\,RT;\] \[\frac{RT}{M}\,=\frac{RV}{w}=\frac{P}{d}\] where d is the density of the gas \[\therefore \,\,{{U}_{rms}}=\sqrt{\frac{3P}{d}}\] at constant pressure, \[{{U}_{rms}}\,\alpha \frac{1}{\sqrt{d}}\]
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