A car tire with a 0.057 m3 capacity is pumped up to 300 kPa at 300 K. Following a 10-hour drive, the internal pressure rises to 330 kPa. Treating air as an ideal gas with a molar heat capacity Cv of 21 J/mole.K, what is the resulting change in internal energy per mole__________________?
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Answer: B. 630
Explanation
Applying the first law of thermodynamics allows calculation of internal energy changes for closed systems. Molar heat capacity at constant volume relates temperature variations directly to internal energy modifications. Ideal gas relationships bridge the initial and final pressure and temperature states effectively. Internal energy change for an ideal gas depends solely on its temperature variation during the process. Molar heat capacity measures the thermal energy required to raise one mole of gas by one kelvin. Combining ideal gas laws with thermodynamic energy balances yields the specified energy value.
Automotive tire pressures increase during long drives due to frictional heating and air compression. Thermodynamic analysis of closed gaseous systems is fundamental for designing pneumatic equipment. Engineers evaluate internal energy shifts to predict thermal stress in pressurized containment vessels. Option A underestimates the energy change by failing to incorporate proper molar heat capacity values. Option C overestimates the internal energy variation due to incorrect temperature ratio calculations. Option D represents a computational error in applying the ideal gas state equations.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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