Heat capacity Cv is expressed by__________________?
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Answer: A. (∂E/∂T)V
Explanation
Constant-volume heat capacity is defined thermodynamically as internal energy derivative with temperature. Holding volume constant ensures all added heat increases internal energy without boundary work. Partial differentiation of internal energy with temperature at constant volume yields heat capacity Cv. Heat capacity measures how much thermal energy a system stores per unit temperature rise. Partial derivatives describe rates of change in multivariable thermodynamic systems. Constant-volume conditions eliminate mechanical work terms from first law energy balances.
Chemical engineers use constant-volume heat capacity in closed rigid vessel thermodynamic calculations. Internal energy tables rely on these partial derivative definitions for property estimations. Designing pressure relief systems requires accurate knowledge of constant-volume thermal properties. Derivative of internal energy with volume at constant temperature measures internal pressure. Derivative of internal energy with pressure at constant volume has no standard heat capacity meaning. Derivative of volume with temperature at constant pressure defines the thermal expansion coefficient.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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