Density of Water at 1°C & 8°C | Homework Help

[nicky670]

Homework Statement:: The relative density of water is determined by the rate at which it expands (and contracts) with changes in temperature. At approximately what other temperature T does water have the same density as at 1 ∘C ?
Relevant Equations:: Just looking at graphical and analyzing. But i can't seem to figure out why the answer is 8 degree celsius.

 

[kuruman]

Do you know at what temperature the water's density is highest? It's a bit difficult to read it from the graph.

 

[sophiecentaur]

Hi and welcome to PF
The relevant region of the graph is very tiny but look at what the graph is telling you. At 0°C it is contracting (negative sign for β) by about 50 per degree. Where is it expanding by 50 per degree? What does that say about where the maximum density is and what would the Density / temperature graph look like?
I think it would be perfectly in order for you to Search about the way the density of water changes with temperature, near freezing point and relate that to the graph.
I don't need to give you the actual answer to your question now, do I?

 

[berkeman]

And what is $\beta$ and why does that look different from the other graphs of Density vs. Temperature for water that you can find at Google Images?

http://oer2go.org/mods/en-boundless...mages/water-density-vs-temperature/index.html

 

[sophiecentaur]

@nicky670 that could be seen as a tricky question to be presented with unless you are familiar with Calculus and the meanings of differentials. It was easy for me / PF because we knew the answer already and it was mainly a matter of reconciling the answer with the graph (reverse process of how you're supposed to do it )

 

[nicky670]

Do you know at what temperature the water's density is highest? It's a bit difficult to read it from the graph.

No it is not stated

 

[nicky670]

Hi and welcome to PF
The relevant region of the graph is very tiny but look at what the graph is telling you. At 0°C it is contracting (negative sign for β) by about 50 per degree. Where is it expanding by 50 per degree? What does that say about where the maximum density is and what would the Density / temperature graph look like?
I think it would be perfectly in order for you to Search about the way the density of water changes with temperature, near freezing point and relate that to the graph.
I don't need to give you the actual answer to your question now, do I?

will do so and get back to you shortly. Thank you

 

[kuruman]

No it is not stated

You can look it up or read it off the graph that @berkeman provided, it's 4 ^oC. That's where the graph you provided crosses the temperature axis. So if the density is highest at 4 ^oC, what happens to the density if you increase the temperature from 4 ^oC by 1 degree? What happens to the density if you decrease the temperature from 4 ^oC by 1 degree?

 

[sophiecentaur]

No it is not stated

It is implied, though, which is what the question is about. at a maximum or minimum (a turning value) the slope / differential is zero. Where is your graph zero? That is your answer, followed by where the value is similar to the value at 0°C (but opposite sign).
As I hinted previously, it's a matter of understanding the maths / logic of it rather than the Physics.