# Calculate the change of volume from volume expansion coefficient

• Outrageous
In summary, this equation shows that the molar volume (v) is equal to the initial molar volume (v0) multiplied by the exponential of the product of the temperature change (T - T0) and the constant β. This means that if you have the constant β and the change in temperature, you can calculate the change in volume using this equation. However, if the initial volume (v0) is not given, then it is not possible to calculate the change in volume.
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.

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.

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 ?

Outrageous said:
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?

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

Outrageous said:
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.

## 1. What is volume expansion coefficient?

Volume expansion coefficient is a measure of how much a material's volume changes when its temperature changes. It is typically represented by the symbol α (alpha) and is expressed in units of per degree Celsius (or per Kelvin).

## 2. How is volume expansion coefficient calculated?

The volume expansion coefficient can be calculated by dividing the change in volume (ΔV) by the initial volume (V0) and the change in temperature (ΔT). This can be represented by the equation α = (ΔV/V0)/ΔT.

## 3. What factors affect the volume expansion coefficient?

The volume expansion coefficient is affected by the type of material, its chemical composition, and the temperature range in which it is measured. It also varies for different phases of matter (solid, liquid, gas) and can change under high pressure conditions.

## 4. Why is volume expansion coefficient important?

Volume expansion coefficient is an important property to consider in various applications, such as in engineering and materials science. It helps in predicting how materials will behave under different temperature conditions, and is crucial in designing structures and machines that can withstand thermal stress and expansion.

## 5. How is volume expansion coefficient used in real-world situations?

The volume expansion coefficient is used in a variety of real-world situations, such as in designing bridges and buildings, creating temperature-resistant materials for spacecrafts and airplanes, and in the manufacturing of thermometers and other measuring devices. It is also important in understanding the effects of temperature changes on natural phenomena, such as ocean currents and weather patterns.

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