Calculate the Difference in Height of Glycerin and Alcohol

In summary, in an open U-shaped tube where glycerin is poured until the height in both sides is 20 cm and then ethyl alcohol is poured in one side, the difference in height between the top surface of the glycerin and the top surface of the alcohol is 7.46 cm. To solve this, the densities of both liquids (1.13 for glycerin and 0.785 for ethyl alcohol) must be known and used in the equation 1.13h = (20-h)1.13 + 20(0.785), where h represents the height of the glycerin column. The difference in height is found to be 7.46 cm by solving for h.
  • #1
iceman_ch
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Homework Statement



Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do not mix.

What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?


Homework Equations





The Attempt at a Solution



I'm not sure where to go with this one. I would think that they would be the same height. the answer is 7.46 cm I had to request the answer. I have a test today so I stilll need to know how to get the answer.
 
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  • #2
the pressures must be equal on both sides. What you failed to mention were 2 constants needed to solve this, the density of glycerin and that of ethyl alcohol, equal to 1.13 and .785 respectively.

you know that height of two columns must be 40 and that because of difference in density, one side will be all glycerin while the other the entire 20cm of EtOH and some fraction of the 20cm of glycerin. That fraction will be
20-height of glycerin. That enough help?

There may be quicker ways to solve this, but this illustrates principles correctly I believe.
 
  • #3
I still don't understand matmatically how that works out to be 7.46 shouldn't it be 20
 
  • #4
let h=height of glycerin, we will ignore g as in mgh and just deal with densitys since its the same everywhere:

1.13H=(20-H)1.13+20*.785 solve for H
the other side will be what? (hint the two heights =40) The difference what? Draw a picture if needed.
 
Last edited:

1. What is the purpose of calculating the difference in height of glycerin and alcohol?

The purpose of this calculation is to determine the relative densities of glycerin and alcohol. This information can then be used in various experiments and industrial processes.

2. How do you calculate the difference in height between glycerin and alcohol?

To calculate the difference in height, you will need to measure the height of each liquid in a graduated cylinder and subtract the initial height of the alcohol from the final height of the glycerin. This will give you the difference in height between the two liquids.

3. What are the units of measurement used for this calculation?

The units of measurement used for this calculation will depend on the specific system being used. However, common units used for measuring the height of liquids include milliliters (mL) and centimeters (cm).

4. Why is it important to calculate the difference in height accurately?

It is important to calculate the difference in height accurately because it directly affects the accuracy of the relative density measurement. If the difference in height is calculated incorrectly, it can lead to incorrect conclusions and potentially affect the outcome of experiments or processes.

5. What other factors can affect the difference in height between glycerin and alcohol?

The difference in height between glycerin and alcohol can be affected by factors such as temperature, pressure, and impurities in the liquids. It is important to control these factors as much as possible in order to obtain accurate results.

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