(C) The ideal gas equation is given by $PV = nRT$,where $n = \frac{N}{N_A}$. Thus,$PV = \frac{N}{N_A}RT$,which implies $N = \frac{PVN_A}{RT}$.For the

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(C) The ideal gas equation is given by $PV = nRT$,where $n = \frac{N}{N_A}$. Thus,$PV = \frac{N}{N_A}RT$,which implies $N = \frac{PVN_A}{RT}$.For the right part $(N_R)$: $P_R = 2P$,$V_R = 2V$,$T_R = T$.$N_R = \frac{(2P)(2V)N_A}{RT} = \frac{4PVN_A}{RT}$.For the left part $(N_L)$: $P_L = P$,$V_L = V$,$T_L = T$.$N_L = \frac{(P)(V)N_A}{RT} = \frac{PVN_A}{RT}$.The ratio of the number of molecules in the right part to the left part is:$\frac{N_R}{N_L} = \frac{4PVN_A / RT}{PVN_A / RT} = \frac{4}{1}$.Therefore,the ratio is $4:1$.

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

Difficult

An insulated container is divided into two parts by a partition. The same gas is filled in both parts. In the right part,the volume,temperature,and pressure are $2V$,$T$,and $2P$ respectively. In the left part,the same parameters are $V$,$T$,and $P$. What is the ratio of the number of molecules in the right part to the left part?

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

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Class 11 Questions

Class 11

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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

For an ideal gas at constant pressure,if the volume is $V$ at a temperature of $27^{\circ}C$,what will be its final volume when the temperature is increased to $327^{\circ}C$?

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An inverted bell lying at the bottom of a lake $47.6 \ m$ deep has $50 \ cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70 \ cm$ of $Hg$ and density of $Hg = 13.6 \ g/cm^3$)

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The average force applied on the wall of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

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The figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then:

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Boyle's law holds for an ideal gas during

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For an ideal gas at constant pressure,if the volume is $V$ at a temperature of $27^{\circ}C$,what will be its final volume when the temperature is increased to $327^{\circ}C$?

An inverted bell lying at the bottom of a lake $47.6 \ m$ deep has $50 \ cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70 \ cm$ of $Hg$ and density of $Hg = 13.6 \ g/cm^3$)

The average force applied on the wall of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

The figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then:

Boyle's law holds for an ideal gas during

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