Surface area of N spherical droplets?

In summary, the conversation discusses a problem involving atomized gasoline and spherical droplets. The goal is to find the total surface area of the droplets in terms of N. The conversation provides equations for surface area and volume, and discusses how to use them to eliminate N and solve for the surface area. The conversation also mentions incorrect values and units, but ultimately leads to the correct solution.
  • #1
saber1357
67
1

Homework Statement



I have the following problem
Assume that 30.0 cm^3 of gasoline is atomized into N spherical droplets, each with a radius of 2.00 x 10^-3 m. What is the total surface area of these N spherical droplets?

Homework Equations


SA = 4 * pi *r^2
V = 4/3 * pi * r^3

The Attempt at a Solution


SA of each atom is 5.03x10^-9
V = 3.35x10^-14
 
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  • #2
Ok, think about this.

What is the total surface area of all the spheres in terms of N?

What is the total volume of all the spheres in terms of N?

If you can answer these questions you should be able to eliminate N, allowing you to solve for The surface area.
 
  • #3
Have you worked out how many droplets there are?
 
  • #4
Ignoring the fact both SA and V of the droplets are both very wrong and lack units (you can do better than that!). Total volume before equals total volume after. Use that to solve for N.
 
  • #5
The values are wrong...?
I know the units of area of is m sqrd and volume is m cubed, but as far the values go, has my calculator betrayed me?
 
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  • #6
You are given a volume of gasoline and told it is turned into N small spheres. You are given the radius of the spheres and thus you can work out the volume and surface area. You know what the volume is and so you can find out how many droplets there are. Then you can find the total surface area.
 
  • #7
Muahahahahaa! I got it :)
I am going to go ahead and say I love you guys. Thank you for all your help.
Next time you guys are in germany, bring lots of lube.
 
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FAQ: Surface area of N spherical droplets?

How is the surface area of a spherical droplet calculated?

The surface area of a spherical droplet can be calculated using the formula 4πr2, where r is the radius of the droplet.

Does the surface area of a droplet change as it evaporates?

Yes, the surface area of a droplet decreases as it evaporates. This is because as the droplet loses water, its radius decreases, resulting in a smaller surface area.

Is the surface area of a droplet affected by its composition?

Yes, the surface area of a droplet can be affected by its composition. Different substances have different surface tensions, which can impact the shape and size of a droplet, and therefore its surface area.

Can the surface area of a droplet be measured experimentally?

Yes, the surface area of a droplet can be measured experimentally using techniques such as optical microscopy or image analysis. These methods involve capturing an image of the droplet and using software to measure its surface area.

How does the surface area of a droplet affect its behavior?

The surface area of a droplet can affect its behavior in various ways. A larger surface area can lead to faster evaporation and a shorter lifespan of the droplet. It can also impact the rate of diffusion and interactions with other substances in its environment.

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