Based on kinetic molecular theory, the thermal conductivity of a monatomic gas varies in direct proportion to___________________?
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Answer: B. T0.5
Explanation
Kinetic molecular theory links thermal conductivity of monatomic gases directly to molecular speeds. Molecular velocity varies in direct proportion to the square root of absolute temperature. This mathematical derivation proves that thermal conductivity scales proportionally with T raised to 0.5. Kinetic theory treats gases as collections of hard spherical particles in constant random motion. Monatomic gases possess only translational kinetic energy without rotational or vibrational energy modes. Thermal conductivity measures a fluid's ability to conduct heat energy through molecular collisions.
Insulation design engineers use gas thermal conductivity data to minimize heat loss in buildings. Aerospace engineers account for temperature dependent gas properties during atmospheric reentry calculations. Understanding molecular transport properties helps optimize high temperature industrial furnace designs. A direct linear proportionality to T applies to other transport properties rather than this conductivity. A T to the power of 1.5 relationship overestimates the temperature dependency for monatomic gases. A quadratic T squared relationship violates kinetic theory derivations for simple monatomic molecules.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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