(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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For an ideal gas,the density of the gas is $\rho_0$ when the temperature and pressure of the gas are $T_0$ and $P_0$ respectively. When the temperature of the gas is $2 T_0$,its pressure becomes $3 P_0$. The new density will be:

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$A$ perfect gas at $27^{\circ} C$ is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be (in $^{\circ} C$)

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Which relation is correct for the given $P-V$ diagram?

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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 the ratio of the universal gas constant $(R)$ to the Avogadro number $(N_A)$?

$A$ vessel has $8 \ g$ of oxygen at pressure $P$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How many grams of oxygen leak out if the final pressure is $P/4$ and the temperature is $200 \ K$?

For an ideal gas,the density of the gas is $\rho_0$ when the temperature and pressure of the gas are $T_0$ and $P_0$ respectively. When the temperature of the gas is $2 T_0$,its pressure becomes $3 P_0$. The new density will be:

$A$ perfect gas at $27^{\circ} C$ is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be (in $^{\circ} C$)

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