(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 Questions

Class 11

Physics Questions

Chapter

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

If an ideal gas has volume $V$ at $27^{\circ}C$ and it is heated at a constant pressure so that its volume becomes $1.5V$,then the value of the final temperature will be ....... $^{\circ}C$.

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Find the approximate number of molecules contained in a vessel of volume $7 \text{ litres}$ at $0^{\circ}C$ and a pressure of $1.3 \times 10^{5} \text{ Pa}$.

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The molecular weight of a gas is $44$. The volume occupied by $2.2 \, g$ of this gas at $0^\circ C$ and $2 \, atm$ pressure will be ....... $lit$.

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The gas which obeys Boyle's law for the maximum range of temperature is

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The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

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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

If an ideal gas has volume $V$ at $27^{\circ}C$ and it is heated at a constant pressure so that its volume becomes $1.5V$,then the value of the final temperature will be ....... $^{\circ}C$.

Find the approximate number of molecules contained in a vessel of volume $7 \text{ litres}$ at $0^{\circ}C$ and a pressure of $1.3 \times 10^{5} \text{ Pa}$.

The molecular weight of a gas is $44$. The volume occupied by $2.2 \, g$ of this gas at $0^\circ C$ and $2 \, atm$ pressure will be ....... $lit$.

The gas which obeys Boyle's law for the maximum range of temperature is

The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

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