[shafaifer]

I guess this exercise is about calculating surface energy for 1000 water droplets. I have attached exercise + my method of progression, but I do not get the correct answer. I hope for help.


With great love/

Shafaifer

[mjc123]

There seem to be a number of mistakes here.
ΔE = γΔA. Where do you get the 2 from? (A formula for a liquid film with 2 sides?)
Surface area for 1 droplet looks right. Surface area for 1000 droplets is simply 1000 times this. What are you doing?
Then you seem to be subtracting the area of 1 droplet from the (wrong) area of 1000. Not surprisingly, you get the wrong answer.
Read the question. What is it asking for?
What is the surface area of 1000 droplets each of radius 10^-6m?
These 1000 droplets then coalesce into one. What is its radius? (Hint: How does mass vary with radius?) What is its surface area?
What is the change in total surface area? and in surface energy?

[shafaifer]

There seem to be a number of mistakes here.
ΔE = γΔA. Where do you get the 2 from? (A formula for a liquid film with 2 sides?)
Surface area for 1 droplet looks right. Surface area for 1000 droplets is simply 1000 times this. What are you doing?
Then you seem to be subtracting the area of 1 droplet from the (wrong) area of 1000. Not surprisingly, you get the wrong answer.
Read the question. What is it asking for?
What is the surface area of 1000 droplets each of radius 10^-6m?
These 1000 droplets then coalesce into one. What is its radius? (Hint: How does mass vary with radius?) What is its surface area?
What is the change in total surface area? and in surface energy?

Thank you, your great exellency. I have attached a modified attempt in which I take your corrections into consideration the best I can at the moment. I am really close now but I am still without knowledge of how to get the correct result for this great exercise.

[mjc123]

You are still subtracting the area of 1 small droplet from that of 1000 small droplets, and getting 999 small droplets. Do you understand what the question is asking you? You take the 1000 small droplets and combine them into one big droplet. What is the area of THAT droplet?

[shafaifer]

Thank you again, very much

I assumed multiplying the surface area of 1 droplet by 1000 would give you the surface area of 1 coalesced droplet.

/

With great regards

[Borek]

I assumed multiplying the surface area of 1 droplet by 1000 would give you the surface area of 1 coalesced droplet.

That's not how it works.

Volume of the droplets is additive, surface is not.

Imagine having a cube with an edge length 1.

What is its surface?

What is its volume?

Imagine having a cube with an edge length 2.

What is its surface?

What is its volume?

How does the surface scale?

How does the volume scale?

[shafaifer]

Thank you Borek,

If you by method of progression wrote to me how to how to come to the correct result, then I would develop a joy of unlimited dimesions. Time could be saved from the very beginning - for the all of us. Please do not find me greedy now; this is the same method I use for people who has minor knowledge than me at certain points. This is the same method used by some teachers at university I attend.

I have tried now with calculating the volume of 1 sphere, then multiplying by 1000 to get the volume of 1000 droplets. I used this volume to isolate the radius of the new droplet, and I used the radius to calculate the surface area. When surface area of the new droplet was calculated, I subtracted the surface area of 1000 droplets from this new surface area, then inserted in the relation for delta(work). I am still without correct result, however, do you judge my method now to be correct?

With my most hopefully regards, Shafaifer

[mjc123]

This method should give you the right answer, but if you don't show us your working, we can't tell whether you made a simple slip in calculation or a more serious error.

[shafaifer]

This method should give you the right answer, but if you don't show us your working, we can't tell whether you made a simple slip in calculation or a more serious error.

And it does now.

[mjc123]

Good. I hope you develop a joy of unlimited dimensions. 

[shafaifer]

Good. I hope you develop a joy of unlimited dimensions. 

Thank you very much