(D) According to the ideal gas equation,$PV = Nk_B T$,where $N$ is the number of molecules and $k_B$ is the Boltzmann constant.For jar $P$,the equatio

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(D) According to the ideal gas equation,$PV = Nk_B T$,where $N$ is the number of molecules and $k_B$ is the Boltzmann constant.For jar $P$,the equation is: $PV = N_P k_B T$ ... $(i)$For jar $Q$,the equation is: $(2P) \left( \frac{V}{4} \right) = N_Q k_B (2T)$Simplifying the left side: $\frac{PV}{2} = N_Q k_B (2T)$$\Rightarrow PV = 4 N_Q k_B T$ ... $(ii)$Comparing equations $(i)$ and $(ii)$:$N_P k_B T = 4 N_Q k_B T$$N_P = 4 N_Q$Therefore,the ratio of the number of molecules in jar $P$ to those in jar $Q$ is $\frac{N_P}{N_Q} = 4:1$.

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

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$A$ jar $P$ is filled with a gas having pressure,volume,and temperature $P, V, T$ respectively. Another gas jar $Q$ is filled with a gas having pressure $2P$,volume $\frac{V}{4}$,and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is:

MHT CET 2023 All MHT CET

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

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Class 11

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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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$A$ jar $P$ is filled with a gas having pressure,volume,and temperature $P, V, T$ respectively. Another gas jar $Q$ is filled with a gas having pressure $2P$,volume $\frac{V}{4}$,and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is:

Similar Questions

What is Boltzmann's constant?

$28\, g$ of $N_2$ gas is contained in a flask at a pressure of $10\, atm$ and at a temperature of $57^\circ C$. It is found that due to leakage in the flask,the pressure is reduced to half and the temperature is reduced to $27^\circ C$. The quantity of $N_2$ gas that leaked out is

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

The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

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