Q. Two tanks of equal volumes contain equal masses of hydrogen and helium at the same temperature. Then :

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A

The pressure of hydrogen is half that of helium

B

The pressure of hydrogen is double that of helium

C

The translational kinetic energy of all the molecules of hydrogen is double of that of all the molecules of helium

D

The total kinetic energy of all the molecules of hydrogen is more than double of that of all the molecules of helium

Solution:

By gas law $P V=\frac{m}{M} R T$ we can directly find that option (B) is correct. Total translational kinetic energy of a gas depends upon the temperature of the gas and total number of molecules as $E=(3 / 2) N k T$ hence option (C) is correct. Total kinetic energy of a gas is given as $E_{T}=(f / 2) k T$ hence option (D) is also correct.

Questions from Kinetic Theory

1. Which one of the following is not an assumption in the kinetic theory of gases?

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2. A gas at one atmosphere and 100 mL is mixed with another gas of equal moles at 0.5 atm and having volume 50 mL in flask of 1 L. What is their final pressure?

3. Two moles of monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of the mixture at constant volume is

4. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -$20\,{}^{\circ}C$ ? (Atomic mass of $Ar = 39 \,u$ and $He = 400 \,u$)

5. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$, where $K$ is a constant. In this process the temperature of the gas is incresed by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) :

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