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Calculate the change of volume from volume expansion coefficient

by Outrageous
Tags: coefficient, expansion, volume
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Outrageous
#1
Jan2-13, 08:05 AM
P: 375
β= (1/v)(∂v/∂T)constant pressure.
What is the v represent? molar volume?
If I am given the β and the change of temperature, how to calculate the change of volume? or it is not enough information to calculate it?

Thank you.
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jedishrfu
#2
Jan2-13, 08:52 AM
P: 3,002
it seems like you have enough if the change is relatively small so that you could use deltas:

beta * delta T * V =delta V

You'd have to decide on what relatively small means and you have to know what V is.
Outrageous
#3
Jan2-13, 09:15 AM
P: 375
Thank you
Question : a container is filled with mercury at 0 degree Celcius. At temperature 50 degree Celcius , what is the volume of mercury that will spill out ?
β Of mercury is 18*10^(-5) /Celcius

Is this possible to do ?

jedishrfu
#4
Jan2-13, 10:20 AM
P: 3,002
Calculate the change of volume from volume expansion coefficient

Quote Quote by Outrageous View Post
Thank you
Question : a container is filled with mercury at 0 degree Celcius. At temperature 50 degree Celcius , what is the volume of mercury that will spill out ?
β Of mercury is 18*10^(-5) /Celcius

Is this possible to do ?
What do you think? A delta of 50 degrees is pretty significant.

What is the initial volume?
Outrageous
#5
Jan2-13, 05:50 PM
P: 375
The initial volume is not given , so that question can't be solved?
Chestermiller
#6
Jan2-13, 08:14 PM
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Quote Quote by Outrageous View Post
β= (1/v)(∂v/∂T)constant pressure.
What is the v represent? molar volume?
If I am given the β and the change of temperature, how to calculate the change of volume? or it is not enough information to calculate it?

Thank you.
Rewriting your equation:

[tex]\frac{d\ln{v}}{dt}=\beta[/tex]

Integrating, you get:

[tex]v=v_0\exp(\beta(T - T_0))[/tex]

where v0 is the volume at temperature T0.


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