(D) The ideal gas equation is given by $PV = NkT$,where $N$ is the number of molecules and $k$ is the Boltzmann constant.For container $A$: $P_A = P$,

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(D) The ideal gas equation is given by $PV = NkT$,where $N$ is the number of molecules and $k$ is the Boltzmann constant.For container $A$: $P_A = P$,$V_A = V$,$T_A = T$. So,$N_A = \frac{PV}{kT}$.For container $B$: $P_B = 2P$,$V_B = V/4$,$T_B = 2T$. So,$N_B = \frac{(2P)(V/4)}{k(2T)} = \frac{PV/2}{2kT} = \frac{PV}{4kT}$.The ratio of the number of molecules is $\frac{N_A}{N_B} = \frac{PV/kT}{PV/4kT} = \frac{4}{1}$.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

For container $A$,the pressure is $P$,volume is $V$,and temperature is $T$. For container $B$,the pressure is $2P$,volume is $V/4$,and temperature is $2T$. Find the ratio of the number of molecules in container $A$ to that in container $B$.

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

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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

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Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under these conditions,the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of the molecular weights of $A$ and $B$ is:

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For container $A$,the pressure is $P$,volume is $V$,and temperature is $T$. For container $B$,the pressure is $2P$,volume is $V/4$,and temperature is $2T$. Find the ratio of the number of molecules in container $A$ to that in container $B$.

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$A$ graph between volume $V$ and absolute temperature $T$ is obtained when a given mass of a gas is heated. During the heating process from state-$1$ to state-$2$,the pressure

When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ} C$,its pressure increases by $0.4 \%$. The initial temperature of the gas is ..........$K$.

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$A$ cylinder contains $10\, kg$ of gas at a pressure of $10^7\, N/m^2$. The quantity of gas taken out of the cylinder,if the final pressure is $2.5 \times 10^6\, N/m^2$,will be ..... $kg$ (Temperature of the gas is constant).

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under these conditions,the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of the molecular weights of $A$ and $B$ is:

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