Mixing Water Masses: Calculating Proportions for Resultant Mass R

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Homework Help Overview

The discussion revolves around calculating the proportions of three water masses mixed to form a resultant mass, focusing on temperature and salinity parameters. The original poster seeks assistance in determining the relative proportions of the water masses based on their respective temperatures and salinities.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting up equations based on the temperatures and salinities of the water masses. There are attempts to formulate relationships between the masses using algebraic expressions, with questions about how to incorporate both temperature and salinity into the calculations.

Discussion Status

Some participants have provided hints and guidance on how to structure the problem, suggesting equations to connect the variables. There is an ongoing exploration of the relationships between the masses, with some participants questioning the correctness of their derived ratios and seeking clarification on the calculations.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for solving the equations. There is also a shift in focus to a different topic regarding the properties of a spherical balloon, indicating a potential branching of the discussion.

groovayness
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Proportions help needed!

Three water masses (I, II, III) are mixed together to form a resultant water mass (R).
I: T=5 deg C, S=35.50 ppt
II: T=2 deg C, S=34.50 ppt
III: T= 1 deg C, S=35.25 ppt
R: T= 3 deg C, S=35.00 ppt
What were the relative proportions of I, II, and III that were mixed together to form R?

Someone please help, I don't even know where to start...
 
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Hi groovayness! :smile:

In questions like this, start by saying:

"Let the mass of I be a, of II be b, and of III be c".

(So the mass of R will be a + b + c.)

Hint: if a combination of a at 5º, b at 2º, and c at 1º, is at 3º … what formula does that give you connecting a b and c? :smile:
 
ok so would the equation be 5a+2b+1c=3(a+b+c)? but then what am i solving for?
And then where do i factor in the salt concentration (s)?
 
Yes, that's right!

Now put the a's b's and c's together, to make 2a = b+ 2c.

And then do the same thing for the salt … then you'll have another equation for a b and c, from which you can find the ration b/c. :smile:
 
ok i think i got it.

i got a:b:c is 3.5 : 5 : 1

is that correct?
 
groovayness said:
ok i think i got it.

i got a:b:c is 3.5 : 5 : 1

is that correct?

Noo … it should be 5 : 6 : 2.

Show us your working. :confused:
 


A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 9.4 during this procedure, by what factor does the radius of the balloon change?

If the radius of a sphere is increased by 12 %, by what factor does its surface area increase?
- By what percentage does its surface area increase?
- By what factor does the sphere's volume increase?
- By what percentage does the sphere's volume increase?

The weight of an object at the surface of a planet is proportional to the planet's mass and inversely proportional to the square of the radius of the planet. Jupiter's radius is 11 times Earth's and its mass is 320 times Earth's. An apple weighs 1.0 N on Earth. How much would it weigh on Jupiter?
 

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