Derivatives Application: Compressibility

in MES Science2 months ago

In this video I go over another derivatives application and show how isothermal compressibility can be described using the derivative as a rate of change of the volume with increasing applied pressure. I also go over an example in determining the compressibility of air at 25 degrees Celsius.


Watch video on:

Download video notes: https://1drv.ms/b/s!As32ynv0LoaIiKtVszaCgz60JI8tZg?e=snqrAM


View Video Notes Below!


Download these notes: Link is in video description.
View these notes as an article: https://peakd.com/@mes
Subscribe via email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate

Reuse of my videos:

  • Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.

Fight back against censorship:

  • Bookmark sites/channels/accounts and check periodically
  • Remember to always archive website pages in case they get deleted/changed.

Join my private Discord chat room: https://mes.fm/chatroom

Check out my Reddit and Voat math forums:

Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow along my epic video series:


NOTE #1: If you don't have time to watch this whole video:

NOTE #2: If video volume is too low at any part of the video:


Derivatives Application: Compressibility

Derivatives Application Example Compressibility.jpeg

Compressibility

One of the quantities of interest in thermodynamics is compressibility. If a given substance is kept at a constant temperature, then its volume V depends on its pressure P.

image.png

We can consider the rate of change of volume with respect to pressure – namely, the derivative dV/dP. As P increases, V decreases, so dV/dP < 0.

image.png

The compressibility is defined by introducing a minus sign and dividing this derivative by the volume V:

image.png

Thus, β measures how fast, per unit volume, the volume of a substance decreases as the pressure on it increases at constant temperature.

Example

If the volume V (in m3) of a sample of air at 25°C was found to be related to the pressure P (in kPa) by the equation:

image.png

Determine the Compressibility of the air at a pressure of 50 kPa.

image.png

image.png