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An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1 = 100 kPa, V1 = 0.2 m3 and p2 = 200 kPa, V2 = 0.1 m3 and the gas constant, R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is______
(Important - Enter only the numerical value in the answer)
Correct answer is '15'. Can you explain this answer?
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Given information:
- Initial conditions: p1 = 100 kPa, V1 = 0.2 m3
- Final conditions: p2 = 200 kPa, V2 = 0.1 m3
- Gas constant: R = 0.275 kJ/kg-K
To find: Magnitude of the work required for the process.
The work done by an ideal gas during a reversible process can be calculated using the equation:
W = ∫p dV
Since the pressure varies linearly with volume, we can express the pressure as a function of volume using the equation of a straight line:
p = p1 + (p2 - p1) * (V - V1) / (V2 - V1)
where p is the pressure and V is the volume.
Substituting this expression for pressure in the integral, we have:
W = ∫(p1 + (p2 - p1) * (V - V1) / (V2 - V1)) dV
Integrating this expression with respect to V, we get:
W = p1 * V + (p2 - p1) * (V - V1) / (V2 - V1) * (V - V1) / 2
Evaluating this expression between the initial and final volumes, we have:
W = p1 * V2 + (p2 - p1) * (V2 - V1) / (V2 - V1) * (V2 - V1) / 2 - p1 * V1
Simplifying this expression, we get:
W = (p1 * V2 - p1 * V1) + (p2 - p1) * (V2 - V1) / 2
Using the given values, we can substitute the numerical values into the equation to find the work done:
W = (100 kPa * 0.1 m3 - 100 kPa * 0.2 m3) + (200 kPa - 100 kPa) * (0.1 m3 - 0.2 m3) / 2
W = -10 kJ + 100 kPa * (-0.1 m3) / 2
W = -10 kJ - 5 kJ
W = -15 kJ
Note that the negative sign indicates that work is done on the gas during this process.
Therefore, the magnitude of the work required for the process is 15 kJ.
- Initial conditions: p1 = 100 kPa, V1 = 0.2 m3
- Final conditions: p2 = 200 kPa, V2 = 0.1 m3
- Gas constant: R = 0.275 kJ/kg-K
To find: Magnitude of the work required for the process.
The work done by an ideal gas during a reversible process can be calculated using the equation:
W = ∫p dV
Since the pressure varies linearly with volume, we can express the pressure as a function of volume using the equation of a straight line:
p = p1 + (p2 - p1) * (V - V1) / (V2 - V1)
where p is the pressure and V is the volume.
Substituting this expression for pressure in the integral, we have:
W = ∫(p1 + (p2 - p1) * (V - V1) / (V2 - V1)) dV
Integrating this expression with respect to V, we get:
W = p1 * V + (p2 - p1) * (V - V1) / (V2 - V1) * (V - V1) / 2
Evaluating this expression between the initial and final volumes, we have:
W = p1 * V2 + (p2 - p1) * (V2 - V1) / (V2 - V1) * (V2 - V1) / 2 - p1 * V1
Simplifying this expression, we get:
W = (p1 * V2 - p1 * V1) + (p2 - p1) * (V2 - V1) / 2
Using the given values, we can substitute the numerical values into the equation to find the work done:
W = (100 kPa * 0.1 m3 - 100 kPa * 0.2 m3) + (200 kPa - 100 kPa) * (0.1 m3 - 0.2 m3) / 2
W = -10 kJ + 100 kPa * (-0.1 m3) / 2
W = -10 kJ - 5 kJ
W = -15 kJ
Note that the negative sign indicates that work is done on the gas during this process.
Therefore, the magnitude of the work required for the process is 15 kJ.
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An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1 = 100 kPa, V1 = 0.2 m3and p2 = 200 kPa, V2 = 0.1 m3 and the gas constant, R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is______(Important - Enter only the numerical value in the answer)Correct answer is '15'. Can you explain this answer?
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An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1 = 100 kPa, V1 = 0.2 m3and p2 = 200 kPa, V2 = 0.1 m3 and the gas constant, R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is______(Important - Enter only the numerical value in the answer)Correct answer is '15'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1 = 100 kPa, V1 = 0.2 m3and p2 = 200 kPa, V2 = 0.1 m3 and the gas constant, R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is______(Important - Enter only the numerical value in the answer)Correct answer is '15'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are: p1 = 100 kPa, V1 = 0.2 m3and p2 = 200 kPa, V2 = 0.1 m3 and the gas constant, R = 0.275 kJ/kg-K. The magnitude of the work required for the process (in kJ) is______(Important - Enter only the numerical value in the answer)Correct answer is '15'. Can you explain this answer?.
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