(C) Using the ideal gas equation: $PV = \frac{m}{M}RT$,where $P$ is pressure,$V$ is volume,$m$ is mass,$M$ is molar mass,$R$ is the universal gas cons

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(C) Using the ideal gas equation: $PV = \frac{m}{M}RT$,where $P$ is pressure,$V$ is volume,$m$ is mass,$M$ is molar mass,$R$ is the universal gas constant,and $T$ is temperature.Since $P$,$V$,$m$,and $R$ are the same for both gases,we have $T = \frac{PVM}{mR}$.This implies $T \propto M$.The molar mass of helium $(M_{He} = 4 \ g/mol)$ is less than the molar mass of nitrogen $(M_{N_2} = 28 \ g/mol)$.Therefore,$T_{helium} < T_{nitrogen}$.

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

You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen?

A
$T_{helium} > T_{nitrogen}$
B
$T_{helium} = T_{nitrogen}$
C
$T_{helium} < T_{nitrogen}$
D
can't be said

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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 given figure represents two isobaric processes for the same mass of an ideal gas. Then:

DifficultJEE MAIN 2024

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The gas which obeys Boyle's law for the maximum range of temperature is

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At $10^{\circ} C$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $110^{\circ} C$,this ratio is:

MediumAIPMT 2008

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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:

Medium

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An ideal gas has pressure $P$,volume $V$ and absolute temperature $T$. If $m$ is the mass of each molecule and $K$ is the Boltzmann constant,then the density of the gas is:

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You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen?

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The given figure represents two isobaric processes for the same mass of an ideal gas. Then:

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