(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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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 figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then:

Medium

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What is the nature of the $P$ versus $1/V$ graph at a constant temperature?

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$A$ metre-long narrow bore held horizontally (and closed at one end) contains a $76 \; cm$ long mercury thread,which traps a $15 \; cm$ column of air. What happens if the tube is held vertically with the open end at the bottom?

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If a given mass of gas occupies a volume of $10\, cc$ at $1\, atm$ pressure and a temperature of $100^{\circ}C$ $(373.15\, K)$,what will be its volume at $4\, atm$ pressure,assuming the temperature remains constant?

Easy

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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

The figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then:

What is the nature of the $P$ versus $1/V$ graph at a constant temperature?

$A$ metre-long narrow bore held horizontally (and closed at one end) contains a $76 \; cm$ long mercury thread,which traps a $15 \; cm$ column of air. What happens if the tube is held vertically with the open end at the bottom?

If a given mass of gas occupies a volume of $10\, cc$ at $1\, atm$ pressure and a temperature of $100^{\circ}C$ $(373.15\, K)$,what will be its volume at $4\, atm$ pressure,assuming the temperature remains constant?

$A$ 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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