For a gas governed by P (V – b) = RT (where b is a positive constant and Cv is constant), its internal energy is a function of its________________?
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Answer: C. Temperature
Explanation
The internal energy depends solely on temperature because the potential energy term remains zero. This behavior mirrors that of an ideal gas despite the presence of volume constant b. Mathematical derivation confirms that partial derivative of internal energy with respect to volume vanishes entirely. Real gases typically experience intermolecular forces which cause internal energy to vary with volume changes. The equation provided modifies the standard ideal gas law by incorporating a constant volume correction factor. Thermodynamic relations allow engineers to calculate exact state properties using such specialized gas equations.
Chemical engineers use modified equations of state to model high pressure industrial gas behaviors accurately. Understanding internal energy dependencies is crucial for designing efficient heat exchangers and closed reactor vessels. Process optimization relies heavily on knowing whether energy states fluctuate with pressure or volume. Pressure does not dictate internal energy values because intermolecular potential energy contributions are effectively canceled out. Volume changes fail to alter internal energy since the specific derivative condition equals absolute zero here. Choosing all options together is incorrect because only temperature dictates the internal energy state directly.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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