(A) Given the pressure-volume relation: $P = \frac{a}{1 + (V/b)^2}$.At $V = b$,the pressure $P$ becomes: $P = \frac{a}{1 + (b/b)^2} = \frac{a}{1 + 1}

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(A) Given the pressure-volume relation: $P = \frac{a}{1 + (V/b)^2}$.At $V = b$,the pressure $P$ becomes: $P = \frac{a}{1 + (b/b)^2} = \frac{a}{1 + 1} = \frac{a}{2}$.Using the ideal gas equation for $n = 1$ mole: $PV = nRT$.Substituting $P = \frac{a}{2}$,$V = b$,and $n = 1$:$(\frac{a}{2}) \times b = 1 \times R \times T$.Solving for $T$: $T = \frac{ab}{2R}$.

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

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

A
$\frac{ab}{2R}$
B
$\frac{ab}{R}$
C
$ab$
D
Zero

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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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$A$ vessel of volume $8\, L$ contains an ideal gas at $300\, K$ and $2\, atm$ pressure. The gas is allowed to leak until the pressure becomes $125\, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.

Medium

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$O_2$ gas is filled in a vessel. If the pressure is doubled and the temperature becomes four times,how many times will its density become?

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An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

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$A$ balloon is filled with $500 \,m^3$ of helium gas at $27^{\circ} C$ and $1 \,atm$ pressure. What will be the volume of the helium gas at $-3^{\circ} C$ and $0.5 \,atm$ pressure (in $\,m^3$)?

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In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

Similar Questions

$A$ 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 $200 \ K$?

$A$ vessel of volume $8\, L$ contains an ideal gas at $300\, K$ and $2\, atm$ pressure. The gas is allowed to leak until the pressure becomes $125\, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.

$O_2$ gas is filled in a vessel. If the pressure is doubled and the temperature becomes four times,how many times will its density become?

An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

$A$ balloon is filled with $500 \,m^3$ of helium gas at $27^{\circ} C$ and $1 \,atm$ pressure. What will be the volume of the helium gas at $-3^{\circ} C$ and $0.5 \,atm$ pressure (in $\,m^3$)?

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