Gas pressure expressed in terms of its mean kinetic energy per unit volume E equals________________?
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Answer: D. 2E/3
Explanation
Kinetic theory of gases relates macroscopic pressure to molecular translational kinetic energy per unit volume. Mathematical derivation from statistical mechanics proves that pressure equals two-thirds of this kinetic energy. This fundamental equation bridges microscopic molecular motion with macroscopic thermodynamic pressure. Mean kinetic energy per unit volume is denoted as E, representing molecular motion intensity. Pressure results from elastic collisions of gas molecules against enclosing container boundary walls. Ideal gas temperature is directly proportional to this average molecular kinetic energy.
Physics and thermodynamics courses use kinetic theory to explain macroscopic gas laws from molecular behavior. Astrophysics applications utilize kinetic pressure relations to model stellar atmospheres and gas nebulas. Understanding molecular energy distribution helps engineers calculate sound speeds in compressible fluids. Dividing kinetic energy by three underestimates the pressure relationship derived from molecular momentum transfer. Dividing energy by two does not match the statistical mechanics factor derived for three-dimensional molecular motion. Three-quarters represents an incorrect coefficient that violates the fundamental kinetic pressure derivation.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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