(C) Average speed $v_{av} = \frac{0 + 2 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 9}{10} = \frac{42}{10} = 4.2 \ m/s$.$rms$ speed $v_{rms} = \sqrt{\frac{0^2 + 2^2

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$4.2 \ m/s, 4.77 \ m/s, 4.0 \ m/s$

(C) Average speed $v_{av} = \frac{0 + 2 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 9}{10} = \frac{42}{10} = 4.2 \ m/s$.$rms$ speed $v_{rms} = \sqrt{\frac{0^2 + 2^2 + 3^2 + 4^2 + 4^2 + 4^2 + 5^2 + 5^2 + 6^2 + 9^2}{10}} = \sqrt{\frac{0 + 4 + 9 + 16 + 16 + 16 + 25 + 25 + 36 + 81}{10}} = \sqrt{\frac{228}{10}} = \sqrt{22.8} \approx 4.77 \ m/s$.Most probable speed $v_{mp}$ is the speed that occurs most frequently. Here,$4$ appears three times,which is more than any other value. Thus,$v_{mp} = 4 \ m/s$.

Class 11 Physics Kinetic Theory of Gases Speed (velocity) of Gas (rms, mean and Most probable speed)

Medium

The speeds of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9$. The values of average speed,$rms$ speed,and most probable speed are respectively:

A
$4.1 \ m/s, 4.1 \ m/s, 4.1 \ m/s$
B
$4.5 \ m/s, 4.5 \ m/s, 5.0 \ m/s$
C
$4.2 \ m/s, 4.77 \ m/s, 4.0 \ m/s$
D
$4.2 \ m/s, 5.1 \ m/s, 4.0 \ m/s$

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Kinetic Theory of Gases

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Speed (velocity) of Gas (rms, mean and Most probable speed)

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$:

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The gas having an average speed four times that of $SO_2$ (molecular mass $64$) is

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Let the r.m.s. velocity of a molecule of a given mass of gas be $C_{1}$ at temperature $27^{\circ} C$. When the temperature is increased to $327^{\circ} C$,the r.m.s. velocity is $C_{2}$. Then the ratio $\frac{C_{2}}{C_{1}}$ is

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At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

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At a temperature of $27^{\circ}C$ and a pressure of $1.0 \times 10^5 \, N/m^2$,the $rms$ speed of a gas is $200 \, m/s$. What is the $rms$ speed at a temperature of $127^{\circ}C$ and a pressure of $0.5 \times 10^5 \, N/m^2$?

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The speeds of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9$. The values of average speed,$rms$ speed,and most probable speed are respectively:

Similar Questions

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$:

The gas having an average speed four times that of $SO_2$ (molecular mass $64$) is

Let the r.m.s. velocity of a molecule of a given mass of gas be $C_{1}$ at temperature $27^{\circ} C$. When the temperature is increased to $327^{\circ} C$,the r.m.s. velocity is $C_{2}$. Then the ratio $\frac{C_{2}}{C_{1}}$ is

At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

At a temperature of $27^{\circ}C$ and a pressure of $1.0 \times 10^5 \, N/m^2$,the $rms$ speed of a gas is $200 \, m/s$. What is the $rms$ speed at a temperature of $127^{\circ}C$ and a pressure of $0.5 \times 10^5 \, N/m^2$?

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