(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

We write the relation for Boyle's law in the form $PV = C$ when the temperature remains constant. In this relation,the magnitude of $C$ depends upon

Easy

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Two vessels $A$ and $B$ are of the same size and are at the same temperature. Vessel $A$ contains $1 \ g$ of hydrogen and vessel $B$ contains $1 \ g$ of oxygen. If $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively,then the ratio $\frac{P_{A}}{P_{B}}$ is:

DifficultJEE MAIN 2024

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One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$, where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).

MediumTS EAMCET 2018

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When air is filled in a balloon, both the pressure and volume increase while the temperature remains constant. Why is Boyle's law not obeyed in this case?

Easy

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One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V,$ and temperature $T.$ If the temperature is increased by $1 \, K$ keeping pressure constant,the increase in volume is

Medium

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We write the relation for Boyle's law in the form $PV = C$ when the temperature remains constant. In this relation,the magnitude of $C$ depends upon

Two vessels $A$ and $B$ are of the same size and are at the same temperature. Vessel $A$ contains $1 \ g$ of hydrogen and vessel $B$ contains $1 \ g$ of oxygen. If $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively,then the ratio $\frac{P_{A}}{P_{B}}$ is:

When air is filled in a balloon, both the pressure and volume increase while the temperature remains constant. Why is Boyle's law not obeyed in this case?

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