An Oxygen Molecule $\mathrm { O } _ { 2 } ,$

question 60

Multiple Choice

An oxygen molecule, $\mathrm { O } _ { 2 } ,$ falls in a vacuum. From what height must it fall so that its translational kinetic energy at the bottom of its fall equals the average translational kinetic energy of an oxygen molecule at 920 K? The mass of one $\mathrm { O } _ { 2 }$ molecule is $5.312 \times 10 ^ { - 26 } \mathrm {~kg}$ and the Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$ Neglect air resistance and assume that g remains constant at $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ throughout the fall of the molecule.

• A) 5.2 km
• B) 12 km
• C) 49 km
• D) 37 km
• E) 24 km

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Definitions:

Economies of Scale

The cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output generally decreasing with increasing scale as fixed costs are spread out over more units of output.

Constant Returns

A situation in production where increasing the inputs by any proportionate amount results in an equal proportionate increase in outputs.

Production Costs

The total expense incurred in manufacturing a product or providing a service, including labor, materials, and overhead costs.

Average Total Cost

The overall expenditure on production when split by the volume of products made.