(C) Since the temperature $T$ and volume $V$ of the vessel remain constant,we use the ideal gas law $PV = nRT$.From this,$n = \frac{PV}{RT}$. Since $V

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$20\%$ of the gas escaped due to the leakage

(C) Since the temperature $T$ and volume $V$ of the vessel remain constant,we use the ideal gas law $PV = nRT$.From this,$n = \frac{PV}{RT}$. Since $V, R,$ and $T$ are constant,$n \propto P$.Initial state: $P_1 = 5 \text{ atm}$,$n_1 = n$.Final state: $P_2 = 4 \text{ atm}$,$n_2 = n'$.Therefore,$\frac{n'}{n} = \frac{P_2}{P_1} = \frac{4}{5} = 0.8$.This means $n' = 0.8n$.The amount of gas that escaped is $\Delta n = n - n' = n - 0.8n = 0.2n$.Percentage of gas escaped = $\frac{0.2n}{n} \times 100\% = 20\%$.

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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$A$ gas is enclosed in a vessel at a constant temperature at a pressure of $5 \text{ atm}$ and volume $4 \text{ L}$. Due to a leakage in the vessel,after some time,the pressure is reduced to $4 \text{ atm}$. As a result,the:

A
volume of the gas decreased by $20\%$
B
average $K.E.$ of gas molecule decreases by $20\%$
C
$20\%$ of the gas escaped due to the leakage
D
$25\%$ of the gas escaped due to the leakage

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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

$A$ 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 $200 \ K$?

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

MediumAIEEE 2012

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Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature $T$. Bulb $2$ is heated to maintain a temperature $2 T$,while bulb $1$ remains at temperature $T$. Assume throughout that the heat conduction by the capillary is negligible. Then,the ratio of final mass of the gas in bulb $2$ to the initial mass of the gas in the same bulb is close to

DifficultKVPY 2011

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The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. Another gas in jar $B$ has pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in jar $A$ to jar $B$ is:

MediumAIIMS 1982

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The pressure of a given mass of gas at $20^{\circ}C$ is $P$. At constant volume,at what temperature in $^{\circ}C$ will the pressure of the gas become $2P$?

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$A$ gas is enclosed in a vessel at a constant temperature at a pressure of $5 \text{ atm}$ and volume $4 \text{ L}$. Due to a leakage in the vessel,after some time,the pressure is reduced to $4 \text{ atm}$. As a result,the:

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$A$ 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 $200 \ K$?

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

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. Another gas in jar $B$ has pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in jar $A$ to jar $B$ is:

The pressure of a given mass of gas at $20^{\circ}C$ is $P$. At constant volume,at what temperature in $^{\circ}C$ will the pressure of the gas become $2P$?

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