Class 11 Exam > Class 11 Questions > n drops of liquid, each with surface energy E...
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n drops of liquid, each with surface energy E, join to form a single drop. In this process
- a)some energy will be absorbed
- b)energy absorbed is E(n – n2/3)
- c)energy released will be E (n – n2/3)
- d)energy released will be E(22/3 – 1)
Correct answer is option 'C'. Can you explain this answer?
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n drops of liquid, each with surface energy E, join to form a single d...
Understanding Surface Energy in Droplet Coalescence
When n drops of liquid coalesce into a single larger drop, the surface energy changes significantly. Here's a detailed breakdown of the energy dynamics involved in this process.
Surface Energy of Individual Drops
- Each small drop has a surface energy denoted as E.
- The total surface area of n small drops is larger than that of a single larger drop formed from them.
Surface Area Considerations
- The surface area of a single drop with radius R is proportional to R^2.
- When n drops merge, the radius of the new drop, R_new, is related to the volume, which is conserved.
- The radius of the new drop can be represented as R_new = R_old * n^(1/3).
Energy Change During Coalescence
- The initial total surface energy of n drops can be calculated as n * E.
- The surface energy of the newly formed drop is proportional to the surface area of that single drop, which leads to a decrease in total surface energy due to the reduction in surface area.
Energy Released Calculation
- The energy released during coalescence is given by the difference in surface energy before and after the process.
- The energy released is calculated as E * (n - n^(2/3)).
- This shows that as more drops combine, the energy released increases, confirming option 'C' as the correct choice.
Conclusion
The key takeaway is that when n drops combine to form a single drop, energy is released due to the decrease in surface area, demonstrating the principles of surface energy and thermodynamics in fluid dynamics.
When n drops of liquid coalesce into a single larger drop, the surface energy changes significantly. Here's a detailed breakdown of the energy dynamics involved in this process.
Surface Energy of Individual Drops
- Each small drop has a surface energy denoted as E.
- The total surface area of n small drops is larger than that of a single larger drop formed from them.
Surface Area Considerations
- The surface area of a single drop with radius R is proportional to R^2.
- When n drops merge, the radius of the new drop, R_new, is related to the volume, which is conserved.
- The radius of the new drop can be represented as R_new = R_old * n^(1/3).
Energy Change During Coalescence
- The initial total surface energy of n drops can be calculated as n * E.
- The surface energy of the newly formed drop is proportional to the surface area of that single drop, which leads to a decrease in total surface energy due to the reduction in surface area.
Energy Released Calculation
- The energy released during coalescence is given by the difference in surface energy before and after the process.
- The energy released is calculated as E * (n - n^(2/3)).
- This shows that as more drops combine, the energy released increases, confirming option 'C' as the correct choice.
Conclusion
The key takeaway is that when n drops combine to form a single drop, energy is released due to the decrease in surface area, demonstrating the principles of surface energy and thermodynamics in fluid dynamics.
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n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer?.
n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for n drops of liquid, each with surface energy E, join to form a single drop. In this process a)some energy will be absorbed b)energy absorbed is E(n – n2/3) c)energy released will be E (n – n2/3)d)energy released will be E(22/3 – 1)Correct answer is option 'C'. Can you explain this answer?.
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