(B) Given the law for the ideal gas process: $VP^2 = K$ (where $K$ is a constant).From the ideal gas equation, we have $PV = nRT$, which implies $P =

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(B) Given the law for the ideal gas process: $VP^2 = K$ (where $K$ is a constant).From the ideal gas equation, we have $PV = nRT$, which implies $P = \frac{nRT}{V}$.Substituting this into the given law:$V \left( \frac{nRT}{V} \right)^2 = K$$V \left( \frac{n^2 R^2 T^2}{V^2} \right) = K$$\frac{n^2 R^2 T^2}{V} = K$Since $n$ and $R$ are constants, we can write $T^2 \propto V$, or $T \propto \sqrt{V}$.Therefore, $\frac{T_2}{T_1} = \sqrt{\frac{V_2}{V_1}}$.Given $V_1 = V$, $T_1 = T$, and $V_2 = 2V$, we have:$\frac{T'}{T} = \sqrt{\frac{2V}{V}} = \sqrt{2}$.Thus, $T' = \sqrt{2} T$.

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

During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

A
$T' = \sqrt{4} T$
B
$T' = \sqrt{2} T$
C
$T' = \sqrt{5} T$
D
$T' = \sqrt{6} T$

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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

Molar volume is the volume occupied by $1 \; mol$ of any (ideal) gas at standard temperature and pressure ($STP$: $1 \; atm$ pressure,$0^{\circ} C$). Show that it is $22.4 \; L$.

Easy

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One mole of a gas at a pressure $2 \ Pa$ and temperature $27^{\circ} C$ is heated until both pressure and volume are doubled. What is the final temperature of the gas (in $K$)?

MediumAP EAMCET 2021

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Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

Medium

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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:

Medium

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The gas in a vessel is subjected to a pressure of $20 \ atm$ at a temperature of $27^{\circ}C$. If one-half of the gas is released from the vessel and the temperature of the remaining gas is raised by $50^{\circ}C$,the final pressure of the gas in the vessel is ....... $atm$.

Medium

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During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

Similar Questions

Molar volume is the volume occupied by $1 \; mol$ of any (ideal) gas at standard temperature and pressure ($STP$: $1 \; atm$ pressure,$0^{\circ} C$). Show that it is $22.4 \; L$.

One mole of a gas at a pressure $2 \ Pa$ and temperature $27^{\circ} C$ is heated until both pressure and volume are doubled. What is the final temperature of the gas (in $K$)?

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

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 gas in a vessel is subjected to a pressure of $20 \ atm$ at a temperature of $27^{\circ}C$. If one-half of the gas is released from the vessel and the temperature of the remaining gas is raised by $50^{\circ}C$,the final pressure of the gas in the vessel is ....... $atm$.

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