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Air is enclosed inside a rigid vessel at the initial temperature 1000K and pressure 4 bar is employed as a heat source. What is the maximum work in kJ/kg that can be developed by operating a heat engine, assuming the atmospheric pressure is 1 bar and temperature is 300K.
- a)243
- b)243.5
Correct answer is between '243,243.5'. Can you explain this answer?
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Air is enclosed inside a rigid vessel at the initial temperature 1000...
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Air is enclosed inside a rigid vessel at the initial temperature 1000...
Given information:
- Initial temperature of air (T1) = 1000 K
- Initial pressure of air (P1) = 4 bar
- Atmospheric pressure (P2) = 1 bar
- Atmospheric temperature (T2) = 300 K
Assumptions:
- Air is considered an ideal gas
- The process is assumed to be reversible
Step 1: Calculation of Specific Gas Constant (R):
The specific gas constant (R) can be calculated using the equation:
R = R_universal / Molar mass
Given that the molar mass of air (M_air) is approximately 28.97 kg/kmol and the universal gas constant (R_universal) is 8.314 kJ/kmol·K, we can calculate R as follows:
R = 8.314 / 28.97 ≈ 0.286 kJ/kg·K
Step 2: Calculation of Specific Volume (v1) and Specific Volume (v2):
The specific volume (v) can be calculated using the equation:
v = R * T / P
For the initial state (state 1), we have:
v1 = R * T1 / P1 = 0.286 * 1000 / 4 = 71.5 m³/kg
For the final state (state 2), we have:
v2 = R * T2 / P2 = 0.286 * 300 / 1 = 85.8 m³/kg
Step 3: Calculation of Work Done (W):
The work done (W) by the heat engine can be calculated using the equation:
W = (P1 * v1 - P2 * v2) / (1 - compression_ratio)
The compression ratio is defined as the ratio of specific volumes at the beginning and the end of the compression process, given by:
compression_ratio = v1 / v2 = 71.5 / 85.8
Substituting the values, we have:
compression_ratio = 0.833
W = (4 * 71.5 - 1 * 85.8) / (1 - 0.833)
W ≈ 243.405 kJ/kg
Therefore, the maximum work that can be developed by operating the heat engine is approximately 243.405 kJ/kg.
- Initial temperature of air (T1) = 1000 K
- Initial pressure of air (P1) = 4 bar
- Atmospheric pressure (P2) = 1 bar
- Atmospheric temperature (T2) = 300 K
Assumptions:
- Air is considered an ideal gas
- The process is assumed to be reversible
Step 1: Calculation of Specific Gas Constant (R):
The specific gas constant (R) can be calculated using the equation:
R = R_universal / Molar mass
Given that the molar mass of air (M_air) is approximately 28.97 kg/kmol and the universal gas constant (R_universal) is 8.314 kJ/kmol·K, we can calculate R as follows:
R = 8.314 / 28.97 ≈ 0.286 kJ/kg·K
Step 2: Calculation of Specific Volume (v1) and Specific Volume (v2):
The specific volume (v) can be calculated using the equation:
v = R * T / P
For the initial state (state 1), we have:
v1 = R * T1 / P1 = 0.286 * 1000 / 4 = 71.5 m³/kg
For the final state (state 2), we have:
v2 = R * T2 / P2 = 0.286 * 300 / 1 = 85.8 m³/kg
Step 3: Calculation of Work Done (W):
The work done (W) by the heat engine can be calculated using the equation:
W = (P1 * v1 - P2 * v2) / (1 - compression_ratio)
The compression ratio is defined as the ratio of specific volumes at the beginning and the end of the compression process, given by:
compression_ratio = v1 / v2 = 71.5 / 85.8
Substituting the values, we have:
compression_ratio = 0.833
W = (4 * 71.5 - 1 * 85.8) / (1 - 0.833)
W ≈ 243.405 kJ/kg
Therefore, the maximum work that can be developed by operating the heat engine is approximately 243.405 kJ/kg.
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Air is enclosed inside a rigid vessel at the initial temperature 1000K and pressure 4 bar is employed as a heat source. What is the maximum work in kJ/kg that can be developed by operating a heat engine, assuming the atmospheric pressure is 1 bar and temperature is 300K.a)243b)243.5Correct answer is between '243,243.5'. Can you explain this answer?
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