First slide

Law of equipartition of energy

Question

A cylinder contains a mixture of helium and argon gas in equilibrium at $150^{0} C$ . What is the average kinetic energy for each type of gas molecule?

Easy

A

$3.26 \times 10^{- 21} J$
B

$8.76 \times 10^{- 21} J$
C

$6.28 \times 10^{- 21} J$
D

${4.14 × 10}^{- 21} J$

Solution

Both kinds of molecules have the same average kinetic energy as the temperature is same for both the gas molecules.
The average kinetic energy of a molecule, $K = \frac{3}{2} k_{B} T$
$K = \frac{3}{2} (1.38 \times 10^{- 23} J / K) (423 K) = 8.76 \times 10^{- 21} J$

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