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There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ?
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There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is o...
Given Information:
- Radius of soap bubble (initial) = 2.4 × 10^-4 m
- Pressure of air in the cylinder (initial) = 10^5 Pa
- Radius of soap bubble (final) = 0.5 × (2.4 × 10^-4 m)
- Surface tension of soap film = 0.08 Nm^-1
To Find:
Pressure of air in the cylinder (final)
Assumptions:
- The temperature remains constant during the compression process, making it an isothermal process.
- The soap bubble is assumed to be a perfect sphere.
Step 1: Calculate the initial surface area of the soap bubble
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
Substituting the radius of the soap bubble (initial) into the formula:
Surface Area (initial) = 4π(2.4 × 10^-4 m)^2
Step 2: Calculate the initial volume of the soap bubble
The volume of a sphere is given by the formula:
Volume = (4/3)πr^3
Substituting the radius of the soap bubble (initial) into the formula:
Volume (initial) = (4/3)π(2.4 × 10^-4 m)^3
Step 3: Calculate the final volume of the soap bubble
Since the radius of the soap bubble is halved, the final volume can be calculated as:
Volume (final) = (4/3)π(0.5 × 2.4 × 10^-4 m)^3
Step 4: Apply the ideal gas law to find the final pressure
According to the ideal gas law, the initial and final pressure of the air in the cylinder can be related to the initial and final volume of the soap bubble:
P1V1 = P2V2
P1 is the initial pressure (10^5 Pa)
V1 is the initial volume (calculated in Step 2)
P2 is the final pressure (to be determined)
V2 is the final volume (calculated in Step 3)
Solving the equation for P2:
P2 = (P1 * V1) / V2
Step 5: Calculate the final pressure
Substituting the known values into the equation:
P2 = (10^5 Pa * Volume (initial)) / Volume (final)
Step 6: Calculate the final pressure in Pa
Substituting the calculated values into the equation:
P2 = (10^5 Pa * (4/3)π(2.4 × 10^-4 m)^3) / (4/3)π(0.5 × 2.4 × 10^-4 m)^3
Simplifying the equation:
P2 = (10^5 Pa * 2.4 × 10^-4 m^3) / (0.5 × 2.4 × 10^-4 m)^3
P2 = (10^5 Pa * 2.4 × 10^-4 m^3) / (0.5 × 2.4 × 10^-4 m)^3
- Radius of soap bubble (initial) = 2.4 × 10^-4 m
- Pressure of air in the cylinder (initial) = 10^5 Pa
- Radius of soap bubble (final) = 0.5 × (2.4 × 10^-4 m)
- Surface tension of soap film = 0.08 Nm^-1
To Find:
Pressure of air in the cylinder (final)
Assumptions:
- The temperature remains constant during the compression process, making it an isothermal process.
- The soap bubble is assumed to be a perfect sphere.
Step 1: Calculate the initial surface area of the soap bubble
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
Substituting the radius of the soap bubble (initial) into the formula:
Surface Area (initial) = 4π(2.4 × 10^-4 m)^2
Step 2: Calculate the initial volume of the soap bubble
The volume of a sphere is given by the formula:
Volume = (4/3)πr^3
Substituting the radius of the soap bubble (initial) into the formula:
Volume (initial) = (4/3)π(2.4 × 10^-4 m)^3
Step 3: Calculate the final volume of the soap bubble
Since the radius of the soap bubble is halved, the final volume can be calculated as:
Volume (final) = (4/3)π(0.5 × 2.4 × 10^-4 m)^3
Step 4: Apply the ideal gas law to find the final pressure
According to the ideal gas law, the initial and final pressure of the air in the cylinder can be related to the initial and final volume of the soap bubble:
P1V1 = P2V2
P1 is the initial pressure (10^5 Pa)
V1 is the initial volume (calculated in Step 2)
P2 is the final pressure (to be determined)
V2 is the final volume (calculated in Step 3)
Solving the equation for P2:
P2 = (P1 * V1) / V2
Step 5: Calculate the final pressure
Substituting the known values into the equation:
P2 = (10^5 Pa * Volume (initial)) / Volume (final)
Step 6: Calculate the final pressure in Pa
Substituting the calculated values into the equation:
P2 = (10^5 Pa * (4/3)π(2.4 × 10^-4 m)^3) / (4/3)π(0.5 × 2.4 × 10^-4 m)^3
Simplifying the equation:
P2 = (10^5 Pa * 2.4 × 10^-4 m^3) / (0.5 × 2.4 × 10^-4 m)^3
P2 = (10^5 Pa * 2.4 × 10^-4 m^3) / (0.5 × 2.4 × 10^-4 m)^3
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There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ?
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There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ?.
There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ?.
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There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ?, a detailed solution for There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? has been provided alongside types of There is soap bubble of radius 2.4 � 10^-4m in air cylinder which is originally at the pressure of 10^5 pa . The air in the cylinder is now compressed isothermally until the radius of bubble is halved . Calculate now the pressure of air in the cylinder . The surface tension of the soap film is 0.08Nm^-1 ? theory, EduRev gives you an
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