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A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?
- a)1.639
- b)2.639
- c)3.639
- d)4.639
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A cylinder with a movable piston contains 3 moles of hydrogen at stand...
The cylinder is completely insulated from its surroundings. As a result, no heat is exchanged between the system (cylinder) and its surroundings. Thus, the process is adiabatic.
As we know that, the value of the ratio of specific heat for standard gas = 1.40.
For an adiabatic process, we have:
The final volume is compressed to half of its initial volume.
As we know that, the value of the ratio of specific heat for standard gas = 1.40.
For an adiabatic process, we have:
The final volume is compressed to half of its initial volume.
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A cylinder with a movable piston contains 3 moles of hydrogen at stand...
Given:
- A cylinder with a movable piston contains 3 moles of hydrogen gas.
- The gas is at standard temperature and pressure.
- The walls of the cylinder are made of a heat insulator.
- The piston is insulated by having a pile of sand on it.
To find:
The factor by which the pressure of the gas increases when it is compressed to half its original volume.
Solution:
Step 1: Understanding the initial state
- The cylinder contains 3 moles of hydrogen gas.
- The volume of the gas is given as the initial volume.
- The pressure of the gas is the initial pressure.
- The temperature is at standard temperature and pressure.
Step 2: Applying the ideal gas law
The ideal gas law states that PV = nRT, where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin
Step 3: Comparing initial and final states
Let's assume the initial volume is V1 and the final volume is V2 (V2 = V1/2).
From the ideal gas law, we can write:
P1V1 = nRT
P2V2 = nRT
Since n, R, and T are constant, we can equate the two equations:
P1V1 = P2V2
Step 4: Finding the factor by which pressure increases
We want to find the factor by which the pressure increases when the volume is halved. Let's divide the second equation by the first equation:
(P2V2) / (P1V1) = 1/2
Simplifying the equation:
P2 / P1 = 1/2
Therefore, the pressure of the gas decreases to half when the volume is halved.
Step 5: Calculating the factor
To find the factor by which the pressure increases, we can take the reciprocal of the fraction:
P1 / P2 = 2
Therefore, the pressure of the gas increases by a factor of 2 when the volume is halved.
Answer:
The pressure of the gas increases by a factor of 2 when it is compressed to half its original volume. Therefore, the correct answer is option B) 2.639.
- A cylinder with a movable piston contains 3 moles of hydrogen gas.
- The gas is at standard temperature and pressure.
- The walls of the cylinder are made of a heat insulator.
- The piston is insulated by having a pile of sand on it.
To find:
The factor by which the pressure of the gas increases when it is compressed to half its original volume.
Solution:
Step 1: Understanding the initial state
- The cylinder contains 3 moles of hydrogen gas.
- The volume of the gas is given as the initial volume.
- The pressure of the gas is the initial pressure.
- The temperature is at standard temperature and pressure.
Step 2: Applying the ideal gas law
The ideal gas law states that PV = nRT, where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin
Step 3: Comparing initial and final states
Let's assume the initial volume is V1 and the final volume is V2 (V2 = V1/2).
From the ideal gas law, we can write:
P1V1 = nRT
P2V2 = nRT
Since n, R, and T are constant, we can equate the two equations:
P1V1 = P2V2
Step 4: Finding the factor by which pressure increases
We want to find the factor by which the pressure increases when the volume is halved. Let's divide the second equation by the first equation:
(P2V2) / (P1V1) = 1/2
Simplifying the equation:
P2 / P1 = 1/2
Therefore, the pressure of the gas decreases to half when the volume is halved.
Step 5: Calculating the factor
To find the factor by which the pressure increases, we can take the reciprocal of the fraction:
P1 / P2 = 2
Therefore, the pressure of the gas increases by a factor of 2 when the volume is halved.
Answer:
The pressure of the gas increases by a factor of 2 when it is compressed to half its original volume. Therefore, the correct answer is option B) 2.639.
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A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer?
Question Description
A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer?.
A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder with a movable piston contains 3 moles of hydrogen at standard temperatureand pressure. The walls of the cylinder are made of a heat insulator, and the pistonis insulated by having a pile of sand on it. By what factor does the pressure of thegas increase if the gas is compressed to half its original volume?a)1.639b)2.639c)3.639d)4.639Correct answer is option 'B'. Can you explain this answer?.
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