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Kinetic theory relation: pressure vs. kinetic energy density for an ideal gas Complete the statement: The pressure exerted by an ideal gas equals what fraction of the kinetic energy of all molecules per unit volume? Choose the correct fraction.

Difficulty: Medium

one-half
one-third
two-third
three-fourth

Correct Answer: two-third

Explanation:

Concept
Kinetic theory yields p = (2/3) × (total translational kinetic energy per unit volume). Equivalently, the kinetic energy density is (3/2) p.

Derivation sketch
From molecular impacts on walls and isotropic velocity distribution, p = (1/3) ρ c², and kinetic energy density is (1/2) ρ c². Ratio: p / (KE density) = (1/3) / (1/2) = 2/3.

Final Answer
two-third

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