(C) According to the Kinetic Theory of Gases $(KTG)$:$1$. The $r.m.s.$ velocity of gas molecules is given by $V_{rms} = \sqrt{\frac{3RT}{M_m}}$. Since

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(C) According to the Kinetic Theory of Gases $(KTG)$:$1$. The $r.m.s.$ velocity of gas molecules is given by $V_{rms} = \sqrt{\frac{3RT}{M_m}}$. Since the temperature $T$ and the molar mass $M_m$ are the same for both vessels,the $r.m.s.$ velocity is the same. Thus,statement $A$ is correct.$2$. From the ideal gas equation $PV = NkT$,where $N$ is the number of molecules and $k$ is the Boltzmann constant,we have $P = \frac{NkT}{V}$. Since $V$,$T$,and $k$ are constant,$P \propto N$. Therefore,the ratio of pressures is $\frac{P_1}{P_2} = \frac{N_1}{N_2} = 1:4$. Thus,statement $B$ is correct.Since statements $A$ and $B$ are correct,the correct option is $C$.

Class 11 Physics Kinetic Theory of Gases Mix Examples-Kinetic Theory of Gases

Medium

The same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$,then:
$A.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be the same.
$B.$ The ratio of pressure in these vessels will be $1:4$.
$C.$ The ratio of pressure will be $1:1$.
$D.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be in the ratio of $1:4$.

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A
$A$ and $C$ only
B
$B$ and $D$ only
C
$A$ and $B$ only
D
$C$ and $D$ only

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Kinetic Theory of Gases

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Mix Examples-Kinetic Theory of Gases

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$A$ vessel contains $14 \, g$ ($7$ moles) of hydrogen and $96 \, g$ ($3$ moles) of oxygen at $STP$. $A$ chemical reaction is induced by passing an electric spark in the vessel until one of the gases is consumed. The temperature is brought back to its starting value of $273 \, K$. The pressure in the vessel is ...... $atm$.

Medium

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In the kinetic theory of gases,which of the following statements regarding elastic collisions of the molecules is wrong?

Easy

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The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas,as a function of temperature $(T)$,qualitatively,is (Graphs are schematic and not drawn to scale)

MediumJEE MAIN 2020

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Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.
Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

MediumAIIMS 2015

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Fill in the blanks:
$(i)$ At low $......$ and high $......$ temperature,real gases behave as an ideal gas.
$(ii)$ $......$ is a measure of the average kinetic energy of a gas.
$(iii)$ The kinetic energy of a gas with mass $m$ is $E$. Its momentum will be $......$.
$(iv)$ At $......$ temperature,$v_{rms}$ will be double that of $v_{rms}$ at $0^{\circ} C$.

Medium

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In the kinetic theory of gases,which of the following statements regarding elastic collisions of the molecules is wrong?

The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas,as a function of temperature $(T)$,qualitatively,is (Graphs are schematic and not drawn to scale)

Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

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Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.
Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.