(D) From the ideal gas equation,the number of molecules $N$ is given by $N = \frac{PV}{kT}$.For compartment $I$,the parameters are $P, V, T$. Thus,the

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(D) From the ideal gas equation,the number of molecules $N$ is given by $N = \frac{PV}{kT}$.For compartment $I$,the parameters are $P, V, T$. Thus,the number of molecules $N_I = \frac{PV}{kT}$.For compartment $II$,the parameters are $2P, 2V, T$. Thus,the number of molecules $N_{II} = \frac{(2P)(2V)}{kT} = 4 \frac{PV}{kT} = 4N_I$.The ratio of the number of molecules in compartments $I$ and $II$ is $\frac{N_I}{N_{II}} = \frac{N_I}{4N_I} = \frac{1}{4}$.

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

Medium

$A$ partition divides a container having insulated walls into two compartments $I$ and $II$. The same gas fills the two compartments. Based on the values given in the figure,the ratio of the number of molecules in compartments $I$ and $II$ is

A
$1:6$
B
$6:1$
C
$4:1$
D
$1:4$

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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

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line:

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Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

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Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then:

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The volume-temperature graph at atmospheric pressure for a monoatomic gas ($V$ in $m^3$,$T$ in $^{\circ}C$) is:

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What is the number of oxygen molecules in a cylinder of volume $1 \ m^3$ at $27^{\circ}C$ and $13.8 \ Pa$? (Boltzmann constant $k = 1.38 \times 10^{-23} \ JK^{-1}$)

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$A$ partition divides a container having insulated walls into two compartments $I$ and $II$. The same gas fills the two compartments. Based on the values given in the figure,the ratio of the number of molecules in compartments $I$ and $II$ is

Similar Questions

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line:

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then:

The volume-temperature graph at atmospheric pressure for a monoatomic gas ($V$ in $m^3$,$T$ in $^{\circ}C$) is:

What is the number of oxygen molecules in a cylinder of volume $1 \ m^3$ at $27^{\circ}C$ and $13.8 \ Pa$? (Boltzmann constant $k = 1.38 \times 10^{-23} \ JK^{-1}$)

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