Relative Density of Glycerin: 66 kg / 1000kg/m3 = 0.066

[Nanu Nana]

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)

 

[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?

 

[Nanu Nana]

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?

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

 

[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.

 

[Merlin3189]

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

 

[Nanu Nana]

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

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

 

[Nanu Nana]

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

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

 

[Merlin3189]

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

 

[Nanu Nana]

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

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

 

[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 = ?

 

[Nanu Nana]

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 = ?

Sorry I don't understand :(

 

[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 RD_glycerin = (density of glycerin) / (density of water) = ? / ? = ?

 

[Nanu Nana]

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 RD_glycerin = (density of glycerin) / (density of water) = ? / ? = ?

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

 

[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 ...

 

[Nanu Nana]

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 ...

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

 

[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

 

[Nanu Nana]

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

Now I get . Thank you very much sir !

d= 63v/50v = 1.260

 

[Merlin3189]

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

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

 

[Nanu Nana]

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

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

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

 

[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 mass_x and mass_w 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.

 

[Nanu Nana]

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 mass_x and mass_w 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.

I was wondering why you didn't gave me correct answer right away . But u did a good thing. I understand it better now .

 

[Ray Vickson]

I was wondering why you didn't gave me correct answer right away . But u did a good thing. I understand it better now .

He is not allowed to do that; it is very much against the PF Rules. Those rules are there precisely so you can make a statement like in your last sentence above!

 

[Nanu Nana]

He is not allowed to do that; it is very much against the PF Rules. Those rules are there precisely so you can make a statement like in your last sentence above!

Oh Sorry I didn't know .Thank you for informing me