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A piston-cylinder device contains 2.2 kg of nitrogen initial nitrogen is now compressed slowly in a polytropic process constant until the volume is reduced by one-half Determin

A piston-cylinder device contains 2.2 kg of nitrogen initial nitrogen is now compressed slowly in a polytropic process constant until the volume is reduced by one-half Determin

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Statement A piston–cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25°C. The nitrogen is now compressed slowly in a polytropic process during which \( PV^{1.3} = \) constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process, in kJ. Use \( R = 0.2968 \, \text{kJ/kg.K} \) and \( C_v = 0.744 \, \text{kJ/kg.K} \). ### Explanation and Calculations 1. **Initial Conditions:** - Mass (\( m \)): 2.2 kg - Initial Pressure (\( P_1 \)): 100 kPa - Initial Temperature (\( T_1 \)): 25°C (or 298 K) 2. **Process Description:** - Polytropic process with \( PV^{1.3} = \) constant. - Volume is reduced by half. 3. **Process Equations:** - Use the ideal gas law for initial state: \[ P_1V_1 = mRT_1 \] - For polytropic processes: \[ W = \frac{P_2V_2 - P_1V_1}{1-n} \] - Use the given \( n = 1.3 \). 4. **Finding Final State and Calculations:** - Use the relationship \( V_2 = \frac{V_1}{2} \). - Substitute \( n \) into the polytropic formula for further calculations. 5. **Heat Transfer:** - Employ the first law of thermodynamics: \[ Q = \Delta U + W \] - Calculate change in internal energy using: \[ \Delta U = mC_v(T_2 - T_1) \] Conduct these calculations step-by-step to find the work done and heat transfer in kJ for the given compression process.
Transcribed Image Text:### Problem Statement A piston–cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25°C. The nitrogen is now compressed slowly in a polytropic process during which \( PV^{1.3} = \) constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process, in kJ. Use \( R = 0.2968 \, \text{kJ/kg.K} \) and \( C_v = 0.744 \, \text{kJ/kg.K} \). ### Explanation and Calculations 1. **Initial Conditions:** - Mass (\( m \)): 2.2 kg - Initial Pressure (\( P_1 \)): 100 kPa - Initial Temperature (\( T_1 \)): 25°C (or 298 K) 2. **Process Description:** - Polytropic process with \( PV^{1.3} = \) constant. - Volume is reduced by half. 3. **Process Equations:** - Use the ideal gas law for initial state: \[ P_1V_1 = mRT_1 \] - For polytropic processes: \[ W = \frac{P_2V_2 - P_1V_1}{1-n} \] - Use the given \( n = 1.3 \). 4. **Finding Final State and Calculations:** - Use the relationship \( V_2 = \frac{V_1}{2} \). - Substitute \( n \) into the polytropic formula for further calculations. 5. **Heat Transfer:** - Employ the first law of thermodynamics: \[ Q = \Delta U + W \] - Calculate change in internal energy using: \[ \Delta U = mC_v(T_2 - T_1) \] Conduct these calculations step-by-step to find the work done and heat transfer in kJ for the given compression process.
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