Prove expansibility / isothermal compressibility

In summary, expansibility is a measure of a substance's ability to expand when heated and is typically expressed as the percentage change in volume per unit increase in temperature. It is inversely related to isothermal compressibility and can be calculated using the formula ΔV/V x ΔT. Expansibility is commonly measured experimentally using a dilatometer and is important in scientific research as it helps predict the behavior of substances when heated or cooled and is crucial in the design and development of various products and processes.
  • #1
Outrageous
374
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β is expansibility , (1/V)(∂V/∂T) at constant temperature
κ is isothermal compressibility , (-1/V)(∂V/∂P) at constant pressure

How to prove (∂P/∂T) at constant V = (β/κ)
Thank you
 
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  • #2
Outrageous said:
β is expansibility , (1/V)(∂V/∂T) at constant temperature
κ is isothermal compressibility , (-1/V)(∂V/∂P) at constant pressure

How to prove (∂P/∂T) at constant V = (β/κ)
Thank you

dV = (∂V/∂T)PdT + (∂V/∂P)TdP

set dV = 0 to evaluate (∂P/∂T)V
 
  • #3
Chestermiller said:
dV = (∂V/∂T)PdT + (∂V/∂P)TdP

set dV = 0 to evaluate (∂P/∂T)V


Understand. Thank you
 

1. What is expansibility?

Expansibility is a measure of a substance's ability to expand when heated. It is typically expressed as the percentage change in volume per unit increase in temperature.

2. How is expansibility related to isothermal compressibility?

Expansibility and isothermal compressibility are inversely related. As expansibility increases, isothermal compressibility decreases, and vice versa.

3. What is the formula for calculating expansibility?

The formula for expansibility is ΔV/V x ΔT, where ΔV is the change in volume and ΔT is the change in temperature.

4. How is expansibility measured experimentally?

Expansibility is typically measured using a dilatometer, which is a device that measures the change in volume of a substance as it is heated.

5. Why is expansibility important in scientific research?

Expansibility is an important property to understand in many fields of science, including thermodynamics, materials science, and chemistry. It can help predict how a substance will behave when heated or cooled, and is crucial in the design and development of various products and processes.

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