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

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

This is a short answer type question as classified in NCERT ExemplarVrms= <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>R</mi> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math> Vrms= <math> <mroot> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow></mrow> </mroot> </math> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math> T1=27oC= 27+273=300KT2=127oC= 127+273= 400K <math> <mfrac> <mrow> <mrow> <mn>100</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>300</mn> </mrow> </mrow> <mrow> <mrow> <mn>400</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> Vrms2= <math> <mfrac> <mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>100</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>200</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mi>m</mi> <mo>/</mo> <mi>s</mi> </math>

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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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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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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?