A gas of rigid diatomic molecules ( f = 5 ) was initially at standard pressure P 0 = 1.013 × 1 0 5 Pa and T 0 = 273 K. The gas was then compressed adiabatically η = 5 times in volume. Find the mea

Question

A gas of rigid diatomic molecules ( f = 5 ) was initially at standard pressure P 0 ​ = 1.013 × 1 0 5 Pa and T 0 ​ = 273 K. The gas was then compressed adiabatically η = 5 times in volume. Find the mean kinetic energy of a rotating molecule in the final state.

TestHub · Accepted Answer

T = T 0 ​ η γ − 1 = 273 × 5 0.4 = 519.7 K. A rigid diatomic molecule has two rotational degrees of freedom, so the rotational energy is 2 × 2 1 ​ k T = k T = 1.38 × 1 0 − 23 × 519.7 = 7.2 × 1 0 − 21 J.

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