At what temperature is the average kinetic energy of a molecule of an ideal monatomic gas equal to 2 J?

univerkov | April 20, 2021 | education

Initial data: Ek (value of the average kinetic energy of the molecule) = 2 * 10 ^ -20 J; monatomic gas (i (number of degrees of freedom) = 3).

Reference data: k (Boltzmann’s constant) = 1.38 * 10 ^ -23 J / K.

The temperature of a given monoatomic gas is determined from the formula: Ek = 3/2 * k * T, whence T = 2Ek / 3k.

Let’s perform the calculation: T = 2 * 2 * 10 ^ -20 / (3 * 1.38 * 10 ^ -23) ≈ 966 K.

Answer: The gas temperature should be 966 K.

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