The molecules of a given mass of a gas have root mean square speeds of 100ms^-1 at 27 C° and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?

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Payal Gupta | Contributor-Level 10

8 months ago

This is a short answer type question as classified in NCERT Exemplar

V_rms= $\sqrt[]{\frac{3 R T}{M}}$

V_rms= $\sqrt[]{T}$

$\frac{V_{r m s 1}}{V_{r m s 2}} = \sqrt[]{\frac{T_{1}}{T_{2}}}$

T₁=27^oC= 27+273=300K

T₂=127^oC= 127+273= 400K

$\frac{100}{V_{r m s 2}} = \sqrt[]{\frac{300}{400}} = \frac{\sqrt[]{3}}{2}$

V_rms²= $\frac{2 * 100}{\sqrt[]{3}} = \frac{200}{\sqrt[]{3}} m / s$

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The molecules of a given mass of a gas have root mean square speeds of 100ms-1 at 27 C° and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?

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