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If pressure inside two soap bubbles are 1.01 and 1.02 atm respectively, then the ratio between their volumes is (Take atmospheric pressure = 1 atm)
- a)2:1
- b)8:1
- c)102:101
- d)(102)3:(103)3
Correct answer is option 'B'. Can you explain this answer?
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If pressure inside two soap bubbles are 1.01 and 1.02 atm respectively...
Given: Pressure inside two soap bubbles = 1.01 atm and 1.02 atm
Atmospheric pressure = 1 atm
To find: Ratio between their volumes
Formula used: Boyle’s law
According to Boyle’s law, at a constant temperature, the product of pressure and volume of a fixed mass of gas is always constant.
Mathematically, P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Solution:
Let the volumes of the two soap bubbles be V1 and V2 respectively.
As per Boyle’s law,
P1V1 = P2V2
Using the given values,
1.01V1 = 1.02V2
Dividing both sides by V1, we get
V2/V1 = 1.01/1.02
Now, we need to take atmospheric pressure into consideration.
Atmospheric pressure = 1 atm
Therefore, the absolute pressure inside the soap bubbles would be:
For the first soap bubble, absolute pressure = 1.01 + 1 = 2.01 atm
For the second soap bubble, absolute pressure = 1.02 + 1 = 2.02 atm
Again using Boyle’s law,
P1V1 = P2V2
2.01V1 = 2.02V2
Dividing both sides by V1, we get
V2/V1 = 2.01/2.02 = 8/9
Therefore, the ratio between the volumes of the two soap bubbles is 8:9.
However, the question is asked with respect to atmospheric pressure, so we need to multiply the ratio with atmospheric pressure.
Ratio with respect to atmospheric pressure = 8/9 * 1 = 8/9
Multiplying both sides by 9, we get
Ratio with respect to atmospheric pressure = 8:9
Hence, the correct answer is option B, i.e., 8:1.
Atmospheric pressure = 1 atm
To find: Ratio between their volumes
Formula used: Boyle’s law
According to Boyle’s law, at a constant temperature, the product of pressure and volume of a fixed mass of gas is always constant.
Mathematically, P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Solution:
Let the volumes of the two soap bubbles be V1 and V2 respectively.
As per Boyle’s law,
P1V1 = P2V2
Using the given values,
1.01V1 = 1.02V2
Dividing both sides by V1, we get
V2/V1 = 1.01/1.02
Now, we need to take atmospheric pressure into consideration.
Atmospheric pressure = 1 atm
Therefore, the absolute pressure inside the soap bubbles would be:
For the first soap bubble, absolute pressure = 1.01 + 1 = 2.01 atm
For the second soap bubble, absolute pressure = 1.02 + 1 = 2.02 atm
Again using Boyle’s law,
P1V1 = P2V2
2.01V1 = 2.02V2
Dividing both sides by V1, we get
V2/V1 = 2.01/2.02 = 8/9
Therefore, the ratio between the volumes of the two soap bubbles is 8:9.
However, the question is asked with respect to atmospheric pressure, so we need to multiply the ratio with atmospheric pressure.
Ratio with respect to atmospheric pressure = 8/9 * 1 = 8/9
Multiplying both sides by 9, we get
Ratio with respect to atmospheric pressure = 8:9
Hence, the correct answer is option B, i.e., 8:1.
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If pressure inside two soap bubbles are 1.01 and 1.02 atm respectively, then the ratio between their volumes is (Take atmospheric pressure = 1 atm)a)2:1b)8:1c)102:101d)(102)3:(103)3Correct answer is option 'B'. Can you explain this answer?
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