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Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will be
- a)same for both
- b)greater for Y
- c)greater for X
- d)not altered from the initial values
Correct answer is option 'B'. Can you explain this answer?
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Two samples of air X and Y having same composition and initially at th...
Compressing two samples of air X and Y
Given:
- Two samples of air X and Y have the same composition.
- Both samples are initially at the same temperature and pressure.
- Both samples are compressed from volume V to V/2.
- Sample X is compressed isothermally.
- Sample Y is compressed adiabatically.
To find:
- The final pressure of both samples.
Solution:
Isothermal Compression:
- Isothermal compression occurs at a constant temperature.
- During this process, the heat is exchanged between the system and the surroundings so that the temperature remains constant.
- Therefore, no change in internal energy occurs during this process.
- As per the ideal gas law, PV = nRT. Thus, for isothermal compression, P1V1 = P2V2.
Adiabatic Compression:
- Adiabatic compression occurs without any heat exchange with the surroundings.
- During this process, the temperature increases as the volume decreases.
- Therefore, the internal energy of the system increases during adiabatic compression.
- As per the ideal gas law, PVγ = constant, where γ is the ratio of specific heats of the gas.
- For adiabatic compression, P1V1γ = P2V2γ.
Comparing the final pressures of air X and Y:
- Both air samples have the same composition and are initially at the same temperature and pressure.
- The same amount of work is done on both samples during compression, as the volumes are halved.
- However, the processes of compression are different.
- Isothermal compression of air X results in a lower final pressure because the temperature remains constant.
- Adiabatic compression of air Y results in a higher final pressure because the temperature increases.
- Therefore, the final pressure of air Y is greater than that of air X.
Answer:
The correct option is (B) greater for Y.
Given:
- Two samples of air X and Y have the same composition.
- Both samples are initially at the same temperature and pressure.
- Both samples are compressed from volume V to V/2.
- Sample X is compressed isothermally.
- Sample Y is compressed adiabatically.
To find:
- The final pressure of both samples.
Solution:
Isothermal Compression:
- Isothermal compression occurs at a constant temperature.
- During this process, the heat is exchanged between the system and the surroundings so that the temperature remains constant.
- Therefore, no change in internal energy occurs during this process.
- As per the ideal gas law, PV = nRT. Thus, for isothermal compression, P1V1 = P2V2.
Adiabatic Compression:
- Adiabatic compression occurs without any heat exchange with the surroundings.
- During this process, the temperature increases as the volume decreases.
- Therefore, the internal energy of the system increases during adiabatic compression.
- As per the ideal gas law, PVγ = constant, where γ is the ratio of specific heats of the gas.
- For adiabatic compression, P1V1γ = P2V2γ.
Comparing the final pressures of air X and Y:
- Both air samples have the same composition and are initially at the same temperature and pressure.
- The same amount of work is done on both samples during compression, as the volumes are halved.
- However, the processes of compression are different.
- Isothermal compression of air X results in a lower final pressure because the temperature remains constant.
- Adiabatic compression of air Y results in a higher final pressure because the temperature increases.
- Therefore, the final pressure of air Y is greater than that of air X.
Answer:
The correct option is (B) greater for Y.
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Community Answer
Two samples of air X and Y having same composition and initially at th...
Compressing air samples X and Y
Given that air samples X and Y have the same composition and are initially at the same temperature and pressure. They are compressed from volume V to V/2. X is compressed isothermally, and Y is compressed adiabatically.
Isothermal compression
Isothermal compression is a process in which the temperature of the gas remains constant during compression. This means that the heat generated during compression is removed from the system, and the temperature remains constant.
Adiabatic compression
Adiabatic compression is a process in which no heat enters or leaves the system during compression. This means that the temperature of the gas increases during compression.
Final pressure of X and Y
The final pressure of X and Y can be determined using the ideal gas law, which states that PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Isothermal compression of X
During isothermal compression of X, the temperature remains constant. Therefore, the final pressure can be calculated using the equation PV = constant. Since the volume is halved, the final pressure of X is twice the initial pressure.
Adiabatic compression of Y
During adiabatic compression of Y, the temperature increases. The final pressure can be calculated using the equation PVγ = constant, where γ is the ratio of specific heats. Since air is a diatomic gas, γ is approximately 1.4. Therefore, the final pressure of Y is greater than the initial pressure.
Conclusion
Hence, the correct answer is option B, i.e., the final pressure of Y is greater than the final pressure of X.
Given that air samples X and Y have the same composition and are initially at the same temperature and pressure. They are compressed from volume V to V/2. X is compressed isothermally, and Y is compressed adiabatically.
Isothermal compression
Isothermal compression is a process in which the temperature of the gas remains constant during compression. This means that the heat generated during compression is removed from the system, and the temperature remains constant.
Adiabatic compression
Adiabatic compression is a process in which no heat enters or leaves the system during compression. This means that the temperature of the gas increases during compression.
Final pressure of X and Y
The final pressure of X and Y can be determined using the ideal gas law, which states that PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Isothermal compression of X
During isothermal compression of X, the temperature remains constant. Therefore, the final pressure can be calculated using the equation PV = constant. Since the volume is halved, the final pressure of X is twice the initial pressure.
Adiabatic compression of Y
During adiabatic compression of Y, the temperature increases. The final pressure can be calculated using the equation PVγ = constant, where γ is the ratio of specific heats. Since air is a diatomic gas, γ is approximately 1.4. Therefore, the final pressure of Y is greater than the initial pressure.
Conclusion
Hence, the correct answer is option B, i.e., the final pressure of Y is greater than the final pressure of X.
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Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer?
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Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer?.
Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two samples of air X and Y having same composition and initially at the same temperature and pressure are compressed from volume V to V/2. X is compressed isothermally and Y adiabatically. Then, the final pressure will bea)same for bothb)greater for Yc)greater for Xd)not altered from the initial valuesCorrect answer is option 'B'. Can you explain this answer?.
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