# Relative density

1. Jan 14, 2016

### Nanu Nana

• Member advised to use the homework template for posts in the homework sections of PF.
A receptacle has a mass of 3 kg when it is empty, 53 kg when it is filled with water, and 66 kg when it is filled with glycerin. Calculate the relative density of glycerine.
I know the formula to find out the relative density.
d= absolute density / reference density ( 1000kg/m3)

2. Jan 14, 2016

### Merlin3189

What do the data tell you about the mass and volume of each liquid?

You say $Relative\ Density_x= \frac{density_x}{reference\ density}$
Do you know another formula for density, relating it to mass and volume?
Can you use that and your data to substitute into your RD formula?

3. Jan 14, 2016

### Nanu Nana

Density is mass / volume but the volume is not given.

4. Jan 14, 2016

### Merlin3189

But the receptacle has a certain volume, even if you don't know what it is. Just use a symbol for it, like v.

5. Jan 14, 2016

### Merlin3189

Also, why is the reference density 1000kg/m3?

6. Jan 14, 2016

### Nanu Nana

Ok so : relative density = 66kg/ v / 1000 kg/ m3 ?

7. Jan 14, 2016

### Nanu Nana

Because it is filled with water. And the reference for water is 1000kg/ m3? or Am I wrong ?

8. Jan 14, 2016

### Merlin3189

Ok. So the 1000 kg/m3 is not helpful here. You have some more info in the data.

9. Jan 14, 2016

### Nanu Nana

I didn't leave out any info . I just copied what was written on my text book

10. Jan 14, 2016

### Merlin3189

Your receptacle has volume = ? It holds mass of glycerin = ? It holds mass of water = ?
Then, from your data, density of glycerin = ? and density of water = ?

11. Jan 14, 2016

### Nanu Nana

Sorry I don't understand :(

12. Jan 14, 2016

### Merlin3189

Given: receptacle mass = 3 kg (empty), 53 kg filled with water, 66 kg filled with glycerin
So: receptacle volume = v , water volume = v, glycerin volume = v
and water mass = ? , glycerin mass = ?
So density of water = ? and density of glycerin = ?
Finally RDglycerin = (density of glycerin) / (density of water) = ? / ? = ?

13. Jan 14, 2016

### Nanu Nana

mass water = 53-3 =50 kg water, mass glycerin = 66-3-53 = 10 kg
density of water = 50kg / v density of glycerin = 10kg/ v

14. Jan 14, 2016

### Merlin3189

mass glycerin = 66-3-53 is not correct.
Mass of water = mass of container full of water - mass of container = 53 - 3 = 50 kg
Mass of glycerin = mass of container full of glycerin ........

15. Jan 14, 2016

### Nanu Nana

mass of glycerin = 66 kg-3kg =63 kg glycerin

16. Jan 14, 2016

### Merlin3189

So now density of glycerin $= \frac{63}{v}$ and density of water $= \frac{50}{v}$ and you can work out RD = density G / density W

17. Jan 14, 2016

### Nanu Nana

Now I get . Thank you very much sir !

d= 63v/50v = 1.260

18. Jan 14, 2016

### Merlin3189

Not quite! You got the right idea, but 63/50 is less than 2

$RD_g =\frac {density_g}{density_w} = \frac{\frac{63}{v}}{\frac{50}{v}}=\frac{63}{50}=$

19. Jan 14, 2016

### Nanu Nana

Yes sorry it was mistake. I did have 1.260 as answer but i mistyped it . Thank you very much. And sorry it took quite long for me to understand

20. Jan 14, 2016

### Merlin3189

Oops! I obviously typed that last post wrongly as well. Anyhow ..
That was a long way round to get there. The crucial thing about this question is that you have equal volumes of the two liquids.
So the ratio of the densities is the same as the ratio of the masses.
$$RD_x = \frac {mass_x}{mass_w}$$ where massx and massw are for equal volumes.

PS. It doesn't matter taking time, so long as you understand in the end. On PF I can't just tell you an answer, I have to try to lead you to it.

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