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Standard XII

Physics

P-T Relationship

The molecules...

Question

The molecules of a given mass of a gas have root mean square speeds of $100$ m $s^{- 1}$ at $27$ $^{o} C$ and $1$ atmospheric pressure. The root mean square speeds of the molecules of the gas at $127$ $^{o} C$ and $2$ atmospheric pressure is?

\frac{200}{\sqrt{3}}

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\frac{100}{\sqrt{3}}

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\frac{400}{3}

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\frac{200}{3}

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Solution

The correct option is B $\frac{200}{\sqrt{3}}$
$v_{r m s} \propto \sqrt{T}$ $T = absolute temperature$
$(\frac{v_{r m s_{1} 2}}{v_{r m s_{1} 1}}) = \sqrt{\frac{T^{2}}{T^{1}}}$
$⟹ {(v_{r m s})}_{2} = 100 \times \sqrt{\frac{400}{300}} = \frac{200}{\sqrt{3}}$
Option $A$ is the correct answer.

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Similar questions

The molecules of a given mass of a gas have root mean square speed of $100 m s^{- 1}$ at $27^{\circ} C$ and 1 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $127^{\circ} C$ and 2 atmospheric pressure?

Q. The root mean square speed of molecules of a given mass of a gas at

27 ° C

and

1

atmosphere pressure is

200 {ms}^{- 1}

. The root mean square speed of molecules of the gas at

127 ° C

and

2

atmosphere pressure is

\frac{x}{\sqrt{3}} {ms}^{- 1}

. The value of

x

will be .

Q. The molecules of a given mass of gas have a root mean square velocity of

200 m . s^{- 1}

27^{0} C

and

1.0 \times 10^{5} N . m^{- 2}

pressure. When the temperature is

127^{0} C

and the pressure

0.5 \times 10^{5} N m^{- 2}

, the root mean square velocity is

m s^{- 1}

, is

Q. A gas bulb of 1 L capacity contains

20 \times 10^{21}

molecules of nitrogen exerting a pressure of 7.57

\times

^{3}

^{- 2}

Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to root mean square speed is 0.82, calculate the most probable speed for these molecules at this temperature.

Q. A gas bulb of

1 l i t r e

capacity contains

2.0 \times 10^{21}

molecules of nitrogen exerting a pressure of

7.57 \times 10^{3} N m^{- 2}

. Calculate the root mean square speed and temperature of the gas molecules. If the ratio of most probable speed to the root mean square speed is

0.82

, calculate the most probable speed of these molecules at this temperature.

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The molecules of a given mass of a gas have root mean square speeds of 100m s−1 at 27 oC and 1 atmospheric pressure. The root mean square speeds of the molecules of the gas at 127 oC and 2 atmospheric pressure is?

The correct option is B 200√3vrms∝√T T=absolute temperature(vrms12vrms11)=√T2T1⟹(vrms)2=100×√400300=200√3Option A is the correct answer.

The molecules of a given mass of a gas have root mean square speeds of $100$ m $s^{- 1}$ at $27$ $^{o} C$ and $1$ atmospheric pressure. The root mean square speeds of the molecules of the gas at $127$ $^{o} C$ and $2$ atmospheric pressure is?

The correct option is B $\frac{200}{\sqrt{3}}$
$v_{r m s} \propto \sqrt{T}$ $T = absolute temperature$
$(\frac{v_{r m s_{1} 2}}{v_{r m s_{1} 1}}) = \sqrt{\frac{T^{2}}{T^{1}}}$
$⟹ {(v_{r m s})}_{2} = 100 \times \sqrt{\frac{400}{300}} = \frac{200}{\sqrt{3}}$
Option $A$ is the correct answer.