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A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process?
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A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDurin...
**Given Data:**
- Mass of air (m): 5 kg
- Initial pressure (P1): 400 kPa
- Initial temperature (T1): 30 °C
- Boundary work done by the system (W_boundary): 15 kJ
- Paddle wheel work done on the system (W_paddle wheel): 3 kJ
**Assumptions:**
- Quasi-equilibrium process: The process occurs slowly enough to maintain equilibrium at each step.
- Isothermal process: The temperature of the air remains constant throughout the process.
- Ideal gas behavior: The air behaves as an ideal gas.
**Calculating Initial and Final Volumes:**
We can use the ideal gas law to calculate the initial and final volumes of the air:
PV = mRT
Where:
- P is the pressure
- V is the volume
- m is the mass
- R is the gas constant
- T is the temperature in Kelvin
Converting the initial temperature from Celsius to Kelvin:
T1 = 30 + 273.15 = 303.15 K
Using the ideal gas law to calculate the initial volume:
V1 = (mRT1) / P1
V1 = (5 kg * 8.314 J/(mol·K) * 303.15 K) / (400,000 Pa)
V1 = 0.308 m³
**Calculating Final Pressure:**
Since the process is isothermal, the final pressure can be calculated using the ideal gas law as well:
V2 = V1 + W_boundary / P1
V2 = 0.308 m³ + 15,000 J / 400,000 Pa
V2 = 0.343 m³
Using the ideal gas law to calculate the final pressure:
P2 = (mRT1) / V2
P2 = (5 kg * 8.314 J/(mol·K) * 303.15 K) / 0.343 m³
P2 = 36,612.4 Pa
**Calculating Heat Transfer:**
Since the process is isothermal, the change in internal energy is zero (ΔU = 0). Therefore, the heat transfer during the process is equal to the sum of the work done on the system and the work done by the system:
Q = W_paddle wheel + W_boundary
Q = 3 kJ + 15 kJ
Q = 18 kJ
Therefore, the heat transfer during this isothermal expansion process is 18 kJ.
- Mass of air (m): 5 kg
- Initial pressure (P1): 400 kPa
- Initial temperature (T1): 30 °C
- Boundary work done by the system (W_boundary): 15 kJ
- Paddle wheel work done on the system (W_paddle wheel): 3 kJ
**Assumptions:**
- Quasi-equilibrium process: The process occurs slowly enough to maintain equilibrium at each step.
- Isothermal process: The temperature of the air remains constant throughout the process.
- Ideal gas behavior: The air behaves as an ideal gas.
**Calculating Initial and Final Volumes:**
We can use the ideal gas law to calculate the initial and final volumes of the air:
PV = mRT
Where:
- P is the pressure
- V is the volume
- m is the mass
- R is the gas constant
- T is the temperature in Kelvin
Converting the initial temperature from Celsius to Kelvin:
T1 = 30 + 273.15 = 303.15 K
Using the ideal gas law to calculate the initial volume:
V1 = (mRT1) / P1
V1 = (5 kg * 8.314 J/(mol·K) * 303.15 K) / (400,000 Pa)
V1 = 0.308 m³
**Calculating Final Pressure:**
Since the process is isothermal, the final pressure can be calculated using the ideal gas law as well:
V2 = V1 + W_boundary / P1
V2 = 0.308 m³ + 15,000 J / 400,000 Pa
V2 = 0.343 m³
Using the ideal gas law to calculate the final pressure:
P2 = (mRT1) / V2
P2 = (5 kg * 8.314 J/(mol·K) * 303.15 K) / 0.343 m³
P2 = 36,612.4 Pa
**Calculating Heat Transfer:**
Since the process is isothermal, the change in internal energy is zero (ΔU = 0). Therefore, the heat transfer during the process is equal to the sum of the work done on the system and the work done by the system:
Q = W_paddle wheel + W_boundary
Q = 3 kJ + 15 kJ
Q = 18 kJ
Therefore, the heat transfer during this isothermal expansion process is 18 kJ.
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A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDurin...
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A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process?
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A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process?.
A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piston cylinder device contains 5 kg of air at 400 kPa and 30'CDuring a quasi equilibrium isothermal expansion process, 15 KJ of boundary wrk done by the system and 3KJ of paddle wheel work is done on the system. The heat transfer during this process?.
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