(C) Since the containers are connected,the pressure $P$ in both containers must be equal,i.e.,$P_X = P_Y$.Using the ideal gas equation $PV = nRT = \fr

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(C) Since the containers are connected,the pressure $P$ in both containers must be equal,i.e.,$P_X = P_Y$.Using the ideal gas equation $PV = nRT = \frac{m}{M}RT$,we get $P = \frac{mRT}{MV}$.For both containers,$P = \frac{mRT}{MV}$ is constant,so $\frac{m_X T_X}{V_X} = \frac{m_Y T_Y}{V_Y}$.Given $V_X = 2V_Y$,$T_X = 200 \, K$,$T_Y = 400 \, K$,and $m_X = m$.Substituting these values: $\frac{m \times 200}{2V_Y} = \frac{m_Y \times 400}{V_Y}$.Simplifying: $\frac{100m}{V_Y} = \frac{400m_Y}{V_Y}$.$100m = 400m_Y \Rightarrow m_Y = \frac{100m}{400} = \frac{m}{4}$.

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

Difficult

In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

A
$\frac{m}{8}$
B
$\frac{m}{6}$
C
$\frac{m}{4}$
D
$\frac{m}{2}$

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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

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

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$2 \, g$ of ${O_2}$ gas is taken at $27^{\circ}C$ and a pressure of $76 \, cm$ of $Hg$. Find the volume of the gas (in liters).

Medium

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The graph of pressure $P$ and volume $V$ of $1 \text{ mole}$ of an ideal gas at constant temperature is:

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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 figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\,K$ and $200\,K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

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In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

Similar Questions

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

$2 \, g$ of ${O_2}$ gas is taken at $27^{\circ}C$ and a pressure of $76 \, cm$ of $Hg$. Find the volume of the gas (in liters).

The graph of pressure $P$ and volume $V$ of $1 \text{ mole}$ of an ideal gas at constant temperature is:

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 figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\,K$ and $200\,K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

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