# Isothermal Compressibility

• z_abideen
In summary, the conversation is about a past paper question for an upcoming exam, specifically question 6b). The definition of isothermal compressibility is given as κT ≡ -(1/V)(∂V/∂P)T and it is also given that κT = P-1. The solution involves substituting and integrating, and the concept of Boyle's law is mentioned as the direction for the integration. The conversation ends with a note of encouragement for the exam.

#### z_abideen

Warned for lack of effort. Please note that we require students to provide their attempted solutions.

No idea...

## The Attempt at a Solution

Does anyone know how to do question 6b)? Its a past paper question for an exam in 2 days and i have literally no idea where to start.

κT ≡ -(1/V)(∂V/∂P)T is given as the definition of isothermal compressibility. You've also been given κT = P-1. Substitute and integrate.

Bystander said:
κT ≡ -(1/V)(∂V/∂P)T is given as the definition of isothermal compressibility. You've also been given κT = P-1. Substitute and integrate.
I tried that but I'm not getting anywhere. do you know how to do it?

Do you know what Boyle's law is? That's where you're trying to go with the integration.

Bystander said:
Do you know what Boyle's law is? That's where you're trying to go with the integration.

is this right?

Very good. Good luck with the exam.

Bystander said:
Very good. Good luck with the exam.
thank you :)

## What is isothermal compressibility?

Isothermal compressibility is a measure of how much a substance's volume changes in response to a change in pressure, while keeping its temperature constant.

## What is the formula for isothermal compressibility?

The formula for isothermal compressibility is KT = -1/V (∂V/∂P)T, where KT is the isothermal compressibility, V is the volume, P is the pressure, and T is the temperature.

## What are some real-life applications of isothermal compressibility?

Isothermal compressibility is important in understanding the behavior of gases, liquids, and solids under different pressures. It is used in various industries such as chemical engineering, geology, and material science to design and optimize processes and products.

## How does isothermal compressibility differ from adiabatic compressibility?

Isothermal compressibility measures how a substance responds to a change in pressure while keeping its temperature constant, whereas adiabatic compressibility measures the change in volume in response to a change in pressure without any heat exchange with the surroundings.

## What factors affect the isothermal compressibility of a substance?

The isothermal compressibility of a substance is affected by its molecular structure, temperature, and pressure. Generally, substances with weaker intermolecular forces have higher isothermal compressibility. Higher temperatures and pressures also tend to decrease isothermal compressibility.