(D) Using the ideal gas equation $PV = Nk_BT$,where $N$ is the number of molecules and $k_B$ is the Boltzmann constant.For container $A$: $N_A = \frac

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(D) Using the ideal gas equation $PV = Nk_BT$,where $N$ is the number of molecules and $k_B$ is the Boltzmann constant.For container $A$: $N_A = \frac{PV}{k_BT}$.For container $B$: $N_B = \frac{(2P)(V/4)}{k_B(2T)} = \frac{PV/2}{2k_BT} = \frac{PV}{4k_BT}$.The ratio of the number of molecules is $\frac{N_A}{N_B} = \frac{PV/k_BT}{PV/4k_BT} = \frac{1}{1/4} = \frac{4}{1}$.

Class 11 Physics Kinetic Theory of Gases Gas Laws (Charles, Boyle's, Avagadro's, Gay Lussacs and Dalton's law) and Ideal gas Equation

Medium

$A$ container $A$ contains a gas at pressure $P$,volume $V$,and temperature $T$. Another container $B$ contains a gas at pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in container $A$ to that in container $B$ is:

A
$1 : 1$
B
$1 : 2$
C
$2 : 1$
D
$4 : 1$

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Class 11

Physics Questions

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Kinetic Theory of Gases

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Gas Laws (Charles, Boyle's, Avagadro's, Gay Lussacs and Dalton's law) and Ideal gas Equation

The equation of state for $n$ moles of an ideal gas is $PV = nRT$, where $R$ is a constant. The $SI$ unit for $R$ is

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The volume of an ideal gas is $1 \, L$ and its pressure is equal to $72 \, cm$ of mercury. It is compressed isothermally until its volume becomes $900 \, cm^3$. What is the change in pressure (stress) of the gas in $cm$ of mercury?

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The pressure-temperature graph for an ideal gas is shown in the figure. At point $A$,the density of the gas is $\rho_0$. What will be the density at point $B$?

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The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$ Molecular weight of oxygen $= 32]$

DifficultAP EAMCET 2002

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Which quantity is constant for two gases of equal volume at the same pressure and temperature?

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$A$ container $A$ contains a gas at pressure $P$,volume $V$,and temperature $T$. Another container $B$ contains a gas at pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in container $A$ to that in container $B$ is:

Similar Questions

The equation of state for $n$ moles of an ideal gas is $PV = nRT$, where $R$ is a constant. The $SI$ unit for $R$ is

The volume of an ideal gas is $1 \, L$ and its pressure is equal to $72 \, cm$ of mercury. It is compressed isothermally until its volume becomes $900 \, cm^3$. What is the change in pressure (stress) of the gas in $cm$ of mercury?

The pressure-temperature graph for an ideal gas is shown in the figure. At point $A$,the density of the gas is $\rho_0$. What will be the density at point $B$?

The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$ Molecular weight of oxygen $= 32]$

Which quantity is constant for two gases of equal volume at the same pressure and temperature?

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