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Ideal Gas Equation

A gas mixture...

Question

A gas mixture consists of molecules of types $A, B$ and $C$ with masses $m_{A} > m_{B} > m_{C}$ . Rank the three types of molecules in decreasing order of

A) Average kinetic energy.

B) rms speeds.

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Solution

A) Average kinetic energy of a molecule

$\frac{E}{N} = \frac{3}{2} K_{B} T$

The average kinetic energy of a molecule is proportional to the absolute temperature of the gas, and it is independent of mass of the molecules.
The average $K . E .$ will be same for $A, B$ and $C$ .

$Final Answer :$

The average $K . E$ will be the same as conditions of temperature and pressure are the same.

B) Root mean square speed:

$v_{r m s} = \sqrt{\frac{3 K_{B} T}{m}}$

$v_{r m s} \propto \frac{1}{\sqrt{m}}$

Given $m_{A} > m_{B} > m_{C}$

Then $v_{C} > v_{B} > v_{A}$

$Final Answer:$ $v_{C} > v_{B} > v_{A}$ .

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Similar questions

A, B

C

m_{A} < m_{B} < m_{C}

m_{1} > m_{2} > m_{3} .

V_{r m s}

¯ K

m_{1} > m_{2} > m_{3} ν_{r m s} . ¯ ¯¯¯ ¯ K

6

c

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