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Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?
- a)2 : 3
- b)3 : 2
- c)1 : 3
- d)3 : 1
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two containers equipped with a massless ideal piston are filled with s...
In the first container:
In the second container:
The ratio of the mass of the gas in the first container to that in the second container is given to be 2 : 3.
Therefore,
This is the required solution.
In the second container:
The ratio of the mass of the gas in the first container to that in the second container is given to be 2 : 3.
Therefore,
This is the required solution.Free Test
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Community Answer
Two containers equipped with a massless ideal piston are filled with s...
Given data:
- Two containers filled with the same monatomic ideal gas.
- The mass ratio of gas in the first container to that in the second container is 2:3.
- The gases are maintained at the same temperature and equal volume.
To find:
The ratio of change in pressure in the first container to that in the second container when the gases are allowed to expand to double the initial volume isothermally.
Solution:
1. Let the initial masses of the gas in the first and second containers be 2m and 3m, respectively.
2. Since the gases are maintained at the same temperature, according to the ideal gas law, the initial pressures in both containers (P1 and P2) are directly proportional to their masses.
3. Let P1 and P2 be the initial pressures in the first and second containers, respectively.
4. The ratio of P1 to P2 is equal to the ratio of the masses of the gas filled in the two containers.
P1/P2 = (2m)/(3m) = 2/3
5. When the gases are allowed to expand to double the initial volume, the final pressures (P'1 and P'2) in both containers are inversely proportional to their volumes.
P'1/P'2 = (1/2)/(1/2) = 1
6. Since the expansion is isothermal, the final temperature (T') remains the same as the initial temperature (T).
7. According to the ideal gas law, for an isothermal process, the product of pressure and volume remains constant.
P1V1 = P'1V'1 (initial)
P2V2 = P'2V'2 (initial)
8. Since the volumes double, V'1 = 2V1 and V'2 = 2V2.
9. Substituting the values of V'1, V'2, and P'1/P'2 in the equations from step 7, we get:
P1V1 = (1/2)P'1(2V1)
P2V2 = (1/2)P'2(2V2)
P'1 = P1
P'2 = P2
10. Therefore, the ratio of change in pressure in the first container to that in the second container is:
P'1/P1 = 1/1 = 1
P'2/P2 = 1/1 = 1
11. Hence, the ratio of change in pressure in the first container to that in the second container is 1:1, which simplifies to 1:1 or 1.
Answer:
The ratio of change in pressure in the first container to that in the second container is 1:1 or 1.
- Two containers filled with the same monatomic ideal gas.
- The mass ratio of gas in the first container to that in the second container is 2:3.
- The gases are maintained at the same temperature and equal volume.
To find:
The ratio of change in pressure in the first container to that in the second container when the gases are allowed to expand to double the initial volume isothermally.
Solution:
1. Let the initial masses of the gas in the first and second containers be 2m and 3m, respectively.
2. Since the gases are maintained at the same temperature, according to the ideal gas law, the initial pressures in both containers (P1 and P2) are directly proportional to their masses.
3. Let P1 and P2 be the initial pressures in the first and second containers, respectively.
4. The ratio of P1 to P2 is equal to the ratio of the masses of the gas filled in the two containers.
P1/P2 = (2m)/(3m) = 2/3
5. When the gases are allowed to expand to double the initial volume, the final pressures (P'1 and P'2) in both containers are inversely proportional to their volumes.
P'1/P'2 = (1/2)/(1/2) = 1
6. Since the expansion is isothermal, the final temperature (T') remains the same as the initial temperature (T).
7. According to the ideal gas law, for an isothermal process, the product of pressure and volume remains constant.
P1V1 = P'1V'1 (initial)
P2V2 = P'2V'2 (initial)
8. Since the volumes double, V'1 = 2V1 and V'2 = 2V2.
9. Substituting the values of V'1, V'2, and P'1/P'2 in the equations from step 7, we get:
P1V1 = (1/2)P'1(2V1)
P2V2 = (1/2)P'2(2V2)
P'1 = P1
P'2 = P2
10. Therefore, the ratio of change in pressure in the first container to that in the second container is:
P'1/P1 = 1/1 = 1
P'2/P2 = 1/1 = 1
11. Hence, the ratio of change in pressure in the first container to that in the second container is 1:1, which simplifies to 1:1 or 1.
Answer:
The ratio of change in pressure in the first container to that in the second container is 1:1 or 1.
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Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer?
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Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. 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 Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer?.
Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. 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 Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice Two containers equipped with a massless ideal piston are filled with same monatomic ideal gas. The ratio of the mass of the gas filled in the first container to that in the second container is 2 : 3. The gases in both the containers are maintained at the same temperature and equal volume. The gases are then allowed to expand to double of the initial volume. If the expansion is carried out isothermally, what will be the ratio of change in the pressure in the first container to that in the second container?a)2 : 3b)3 : 2c)1 : 3d)3 : 1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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