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Two samples A and B of a gas initially at the samepressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically).The final pressure of A is
- a)greater then the final pressure of B
- b)equal to the final pressure of B
- c)less than the final pressure of B
- d)twice the final pressure of B
Correct answer is option 'C'. Can you explain this answer?
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Two samples A and B of a gas initially at the samepressure and tempera...
Explanation:
When a gas is compressed, its temperature and volume decrease, and its pressure increases. The final pressure of the gas depends on the type of compression, whether it is isothermal or adiabatic. Let's analyze both types of compression for samples A and B.
Isothermal Compression:
In an isothermal compression, the temperature of the gas remains constant. Therefore, the pressure and volume of the gas are inversely proportional to each other, according to the Ideal Gas Law. Mathematically, we can write:
PV = nRT (where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature)
If we keep the temperature constant, we get:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively.
For sample A, the compression is isothermal. Therefore, we can write:
P1AV = P2AV/2
For sample B, the compression is adiabatic. Therefore, we can write:
P1BV^γ = P2BV^(γ) /2
where γ is the ratio of specific heats (cp/cv) of the gas, which is greater than 1.
We need to compare the final pressures of samples A and B, i.e., P2A and P2B. We can use the equations above to eliminate V and get:
P2A = 2P1A
P2B = P1BV^(γ) /2^(γ-1)
Since V/2 is less than V, we know that P2A is greater than P1A. However, P2B is not necessarily greater than P1B, because the adiabatic compression leads to a decrease in volume and an increase in temperature. Therefore, we need to compare P2A and P2B directly.
Comparison of Final Pressures:
We can write:
P2A/P2B = (2P1A) / (P1BV^(γ) /2^(γ-1))
= 2P1A / P1BV^(γ) * 2^(1-γ)
We can simplify this expression by canceling out P1 and using the fact that γ is greater than 1:
P2A/P2B = 2 * 2^(1-γ)
= 2^(2-γ)
Since γ is greater than 1, 2-γ is negative. Therefore, 2^(2-γ) is less than 1, which means that P2A is less than P2B. Therefore, the correct answer is option C: the final pressure of sample A is less than the final pressure of sample B.
When a gas is compressed, its temperature and volume decrease, and its pressure increases. The final pressure of the gas depends on the type of compression, whether it is isothermal or adiabatic. Let's analyze both types of compression for samples A and B.
Isothermal Compression:
In an isothermal compression, the temperature of the gas remains constant. Therefore, the pressure and volume of the gas are inversely proportional to each other, according to the Ideal Gas Law. Mathematically, we can write:
PV = nRT (where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature)
If we keep the temperature constant, we get:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively.
For sample A, the compression is isothermal. Therefore, we can write:
P1AV = P2AV/2
For sample B, the compression is adiabatic. Therefore, we can write:
P1BV^γ = P2BV^(γ) /2
where γ is the ratio of specific heats (cp/cv) of the gas, which is greater than 1.
We need to compare the final pressures of samples A and B, i.e., P2A and P2B. We can use the equations above to eliminate V and get:
P2A = 2P1A
P2B = P1BV^(γ) /2^(γ-1)
Since V/2 is less than V, we know that P2A is greater than P1A. However, P2B is not necessarily greater than P1B, because the adiabatic compression leads to a decrease in volume and an increase in temperature. Therefore, we need to compare P2A and P2B directly.
Comparison of Final Pressures:
We can write:
P2A/P2B = (2P1A) / (P1BV^(γ) /2^(γ-1))
= 2P1A / P1BV^(γ) * 2^(1-γ)
We can simplify this expression by canceling out P1 and using the fact that γ is greater than 1:
P2A/P2B = 2 * 2^(1-γ)
= 2^(2-γ)
Since γ is greater than 1, 2-γ is negative. Therefore, 2^(2-γ) is less than 1, which means that P2A is less than P2B. Therefore, the correct answer is option C: the final pressure of sample A is less than the final pressure of sample B.
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Two samples A and B of a gas initially at the samepressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically).The final pressure of A isa)greater then the final pressure of Bb)equal to the final pressure of Bc)less than the final pressure of Bd)twice the final pressure of BCorrect answer is option 'C'. Can you explain this answer?
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Two samples A and B of a gas initially at the samepressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically).The final pressure of A isa)greater then the final pressure of Bb)equal to the final pressure of Bc)less than the final pressure of Bd)twice the final pressure of BCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two samples A and B of a gas initially at the samepressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically).The final pressure of A isa)greater then the final pressure of Bb)equal to the final pressure of Bc)less than the final pressure of Bd)twice the final pressure of BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two samples A and B of a gas initially at the samepressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically).The final pressure of A isa)greater then the final pressure of Bb)equal to the final pressure of Bc)less than the final pressure of Bd)twice the final pressure of BCorrect answer is option 'C'. Can you explain this answer?.
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