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

In summary: Density vs Temperature graphs usually have a differential of zero somewhere along the line because as the temperature increases, the molecules move closer together and the atoms start to repel each other more. That creates a decrease in the density. And if you decrease the temperature, the molecules start to move away from each other again and the atoms start to attract each other, which creates an increase in density.
  • #1
nicky670
21
1
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.

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  • #2
Do you know at what temperature the water's density is highest? It's a bit difficult to read it from the graph.
 
  • #3
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?
 
  • #5
@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 :wink:)
 
  • #6
kuruman said:
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
 
  • #7
sophiecentaur said:
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
 
  • #8
nicky670 said:
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?
 
  • #9
nicky670 said:
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.
 
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Related to Density of Water at 1°C & 8°C | Homework Help

What is the density of water at 1°C?

The density of water at 1°C is 0.99997 grams per cubic centimeter. This is often rounded to 1 gram per cubic centimeter for simplicity.

What is the density of water at 8°C?

The density of water at 8°C is 0.99985 grams per cubic centimeter. This is also often rounded to 1 gram per cubic centimeter.

Why is the density of water at 4°C the highest?

The density of water at 4°C is the highest because this is the temperature at which water molecules are most closely packed together. As the temperature decreases from 4°C, the water molecules start to form a crystalline structure and take up more space, resulting in a decrease in density.

How does the density of water at 1°C and 8°C compare to room temperature?

The density of water at 1°C and 8°C is slightly higher than at room temperature (around 20°C). This is because as the temperature increases, the water molecules have more energy and are able to move around more, resulting in a slightly lower density.

Why is it important to know the density of water at different temperatures?

Knowing the density of water at different temperatures is important for a variety of scientific and practical applications. For example, it is necessary for accurately measuring the volume of a liquid when conducting experiments or for calculating the buoyancy of objects in water. It also has practical uses in industries such as food and beverage production, where precise measurements of liquid volumes are crucial.

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