Volume Change by Pressure: How Does Pressure Affect the Volume of an Object?

[robax25]

Homework Statement

It is necessary to calculate the volume of the coin which has mass 25 kg and how does change its volume when it is necessary to calculate its volume at a depth of 5000m. Compare volume change by pressure with the volume change by pressure with the Volume change by temperature.

Homework Equations

volume at surface, M=25kg ρ=m/v
v=1.294 * 10^-3 m³ density of gold ρ= 19320 kg/m³

The Attempt at a Solution

v=1.294 * 10^-3 m³[/B]
I do not know how to calculate the volume at a depth of 5000m but I have pressure at a depth of 5000m.It is 50.3604 MPA. Now I need to find out Temperature using Pressure.

 

[haruspex]

You will need coefficients for the bulk modulus of the metal and its thermal expansion.
https://www.azom.com/properties.aspx?ArticleID=598
https://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html
Etc.

 

[Chestermiller]

You are not told the temperature? Then how are you supposed to determine it?

 

[robax25]

Actually I need the volume at a water depth of 5000m . I can use Boyle's law to calculate Volume and charl's law to calculate Temperatur

 

[robax25]

I do not how to proceed

 

[Chestermiller]

Actually I need the volume at a water depth of 5000m . I can use Boyle's law to calculate Volume and charl's law to calculate Temperatur

You are dealing with a solid, not a gas.

Do you know the equation for the volume change of a solid as a function of the temperature change and the pressure change?

 

[robax25]

Sorry, I don't know

 

[Chestermiller]

Sorry, I don't know

Do you have a textbook? Otherwise, Google "Bulk compressibility" and "Volumetric thermal expansion."

 

[robax25]

L=αLT however, I do not know the temperature

 

[Chestermiller]

L=αLT however, I do not know the temperature

That's the coefficient of linear thermal expansion. The coefficient of volume expansion is 3 x as high.

I guess you need to look up the temperature of the ocean at a depth of 5000 m.

 

[robax25]

I get it 3 degree Celsius

 

[robax25]

Sorry, I learned this formula in structural Mechanics course but I forget it.

 

[robax25]

here I know only volume and how to proceed?

 

[robax25]

how can I calculate the volume at a water depth 5000m?

 

[robax25]

sorry, I get it but How to calculate volume change by pressure?

 

[haruspex]

sorry, I get it but How to calculate volume change by pressure?

https://en.m.wikipedia.org/wiki/Bulk_modulus
Note, however, that there it quite correctly defines it as response to a small change in pressure. This is because, in principle, the modulus depends on the pressure, so what works for a small change won't work for a large one. But I think you'll have to overlook that subtlety.