Question

(a) Calculate the total rotational kinetic energy of the molecules in $1.00 \mathrm{~mol}$ of a diatomic gas at $300 \mathrm{~K}$. (b) Calculate the moment of inertia of an oxygen molecule $\left(\mathrm{O}_{2}\right)$ for rotation about either the $y$ - or z-axis shown in Fig. 18.18 b. Treat the molecule as two massive points (representing the oxygen atoms) separated by a distance of $1.21 \times 10^{-10} \mathrm{~m} .$ The molar mass of oxygen atoms is $16.0 \mathrm{~g} / \mathrm{mol}$ (c) Find the rms angular velocity of rotation of an oxygen molecule about either the $y$ - or z-axis shown in Fig. 18.18b. How does your answer compare to the angular velocity of a typical piece of rapidly rotating machinery $(10,000$ rev $/ \mathrm{min}) ?$

          (a) Calculate the total rotational kinetic energy of the molecules in $1.00 \mathrm{~mol}$ of a diatomic gas at $300 \mathrm{~K}$. (b) Calculate the moment of inertia of an oxygen molecule $\left(\mathrm{O}_{2}\right)$ for rotation about either the $y$ - or z-axis shown in Fig. 18.18 b. Treat the molecule as two massive points (representing the oxygen atoms) separated by a distance of $1.21 \times 10^{-10} \mathrm{~m} .$ The molar mass of oxygen atoms is $16.0 \mathrm{~g} / \mathrm{mol}$
(c) Find the rms angular velocity of rotation of an oxygen molecule about either the $y$ - or z-axis shown in Fig. 18.18b. How does your answer compare to the angular velocity of a typical piece of rapidly rotating machinery $(10,000$ rev $/ \mathrm{min}) ?$

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