# Calculate the change of volume from volume expansion coefficient

1. ### Outrageous

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.

### Staff: Mentor

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.

3. ### Outrageous

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 ?

### Staff: Mentor

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

What is the initial volume?

5. ### Outrageous

375
The initial volume is not given , so that question can't be solved?

### Staff: Mentor

$$\frac{d\ln{v}}{dt}=\beta$$
$$v=v_0\exp(\beta(T - T_0))$$