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A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then
- a)Compressing the gas isothermally will require more work to be done
- b)Compressing the gas through the adiabatic process will require more work to be done
- c)Compressing the gas isothermally or adiabatically will require the same amount of work
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A gas is compressed isothermally to half of its initial volume. The s...
The area under P-V diagrams represents the work done.
Since the slope of the adiabatic process is greater than the slope of the isothermal process.
On the P-V diagram, Area under adiabatic curve > Area under the isothermal curve.
Work done under an adiabatic process is greater than work done under an isothermal process.
Most Upvoted Answer
A gas is compressed isothermally to half of its initial volume. The s...
Explanation:
When a gas is compressed, work is done on it by an external force to reduce its volume. The amount of work done depends on the process through which the compression is carried out. In this question, the same gas is compressed first through an isothermal process and then through an adiabatic process until its volume is reduced to half. Let's analyze the work done in each case.
Work done in Isothermal Compression:
In isothermal compression, the temperature of the gas is kept constant during the compression process. This is achieved by keeping the gas in contact with a heat reservoir (such as a large water bath) that can absorb or release heat as needed. Since the temperature remains constant, the ideal gas law can be used to relate the pressure, volume, and number of moles of the gas. If the initial pressure, volume, and number of moles of the gas are P1, V1, and n respectively, and the final volume is V2, then the work done on the gas during the isothermal compression can be calculated as follows:
Work done = nRT ln (V2/V1)
where R is the gas constant and T is the constant temperature of the gas during the compression.
In this question, the gas is compressed isothermally to half of its initial volume. Therefore, V2 = V1/2. Substituting this into the equation above, we get:
Work done = nRT ln 2
Work done in Adiabatic Compression:
In adiabatic compression, no heat is allowed to enter or leave the gas during the compression process. This means that the temperature of the gas increases as it is compressed. The relationship between the pressure, volume, and temperature of the gas during an adiabatic process is given by the adiabatic equation:
PV^γ = constant
where γ is the ratio of specific heats of the gas (Cp/Cv). If the initial pressure, volume, and number of moles of the gas are P1, V1, and n respectively, and the final volume is V2, then the work done on the gas during the adiabatic compression can be calculated as follows:
Work done = (P1V1 - P2V2)/(γ - 1)
where P2 is the final pressure of the gas, which can be calculated using the adiabatic equation above.
In this question, the gas is compressed adiabatically to half of its initial volume. Therefore, V2 = V1/2. Using the adiabatic equation above, we can relate the initial and final pressures of the gas as follows:
P2 = P1(V1/V2)^γ = 2^(γ-1) P1
Substituting these values into the equation for work done, we get:
Work done = (P1V1 - 2^(γ-1) P1 V1/2)/(γ - 1) = (1 - 2^(γ-1)/2)(P1V1)/(γ - 1)
Comparison:
To compare the work done in the two processes, we need to compare the expressions for work done in each case. Let's simplify the expressions by canceling out common terms:
Work done in isothermal compression = nRT
When a gas is compressed, work is done on it by an external force to reduce its volume. The amount of work done depends on the process through which the compression is carried out. In this question, the same gas is compressed first through an isothermal process and then through an adiabatic process until its volume is reduced to half. Let's analyze the work done in each case.
Work done in Isothermal Compression:
In isothermal compression, the temperature of the gas is kept constant during the compression process. This is achieved by keeping the gas in contact with a heat reservoir (such as a large water bath) that can absorb or release heat as needed. Since the temperature remains constant, the ideal gas law can be used to relate the pressure, volume, and number of moles of the gas. If the initial pressure, volume, and number of moles of the gas are P1, V1, and n respectively, and the final volume is V2, then the work done on the gas during the isothermal compression can be calculated as follows:
Work done = nRT ln (V2/V1)
where R is the gas constant and T is the constant temperature of the gas during the compression.
In this question, the gas is compressed isothermally to half of its initial volume. Therefore, V2 = V1/2. Substituting this into the equation above, we get:
Work done = nRT ln 2
Work done in Adiabatic Compression:
In adiabatic compression, no heat is allowed to enter or leave the gas during the compression process. This means that the temperature of the gas increases as it is compressed. The relationship between the pressure, volume, and temperature of the gas during an adiabatic process is given by the adiabatic equation:
PV^γ = constant
where γ is the ratio of specific heats of the gas (Cp/Cv). If the initial pressure, volume, and number of moles of the gas are P1, V1, and n respectively, and the final volume is V2, then the work done on the gas during the adiabatic compression can be calculated as follows:
Work done = (P1V1 - P2V2)/(γ - 1)
where P2 is the final pressure of the gas, which can be calculated using the adiabatic equation above.
In this question, the gas is compressed adiabatically to half of its initial volume. Therefore, V2 = V1/2. Using the adiabatic equation above, we can relate the initial and final pressures of the gas as follows:
P2 = P1(V1/V2)^γ = 2^(γ-1) P1
Substituting these values into the equation for work done, we get:
Work done = (P1V1 - 2^(γ-1) P1 V1/2)/(γ - 1) = (1 - 2^(γ-1)/2)(P1V1)/(γ - 1)
Comparison:
To compare the work done in the two processes, we need to compare the expressions for work done in each case. Let's simplify the expressions by canceling out common terms:
Work done in isothermal compression = nRT
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A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer?.
A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Thena)Compressing the gas isothermally will require more work to be doneb)Compressing the gas through the adiabatic process will require more work to be donec)Compressing the gas isothermally or adiabatically will require the same amount of workd)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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