calculate the change of volume from volume expansion coefficient

Outrageous

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

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

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

What do you think? A delta of 50 degrees is pretty significant.

What is the initial volume?

Outrageous

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

Chestermiller

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.