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-   -   Calculate the change of volume from volume expansion coefficient (http://www.physicsforums.com/showthread.php?t=662035)

 Outrageous Jan2-13 08:05 AM

calculate the change of volume from volume expansion coefficient

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.

 jedishrfu Jan2-13 08:52 AM

Re: calculate the change of volume from volume expansion coefficient

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 Jan2-13 09:15 AM

Re: calculate the change of volume from volume expansion coefficient

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 Jan2-13 10:20 AM

Re: calculate the change of volume from volume expansion coefficient

Quote:
 Quote by Outrageous (Post 4215770) 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 Jan2-13 05:50 PM

Re: calculate the change of volume from volume expansion coefficient

The initial volume is not given , so that question can't be solved?

 Chestermiller Jan2-13 08:14 PM

Re: calculate the change of volume from volume expansion coefficient

Quote:
 Quote by Outrageous (Post 4215708) 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.

$$\frac{d\ln{v}}{dt}=\beta$$

Integrating, you get:

$$v=v_0\exp(\beta(T - T_0))$$

where v0 is the volume at temperature T0.

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