How to measure the area of a Clapeyron diagram (pV diagram)?

Click For Summary
SUMMARY

The discussion focuses on methods to measure the area of a Clapeyron diagram (pV diagram). Participants suggest practical techniques such as cutting out the area and weighing it on a sensitive balance, as well as tracing the shape onto squared graph paper to estimate the area by counting squares. Integral calculus is mentioned as a potential tool for those familiar with it, particularly in relation to the P-V equations for the diagram's sides. These methods cater to varying levels of mathematical ability, making them accessible to high school students.

PREREQUISITES
  • Understanding of Clapeyron diagrams and their significance in thermodynamics.
  • Basic knowledge of integral calculus for advanced area calculation methods.
  • Familiarity with measuring tools such as sensitive balances.
  • Experience with graph paper for visual estimation techniques.
NEXT STEPS
  • Research methods for calculating areas under curves using integral calculus.
  • Explore the principles of thermodynamics related to Clapeyron diagrams.
  • Learn about the use of graph paper for estimating areas in geometry.
  • Investigate the calibration process for sensitive balances in scientific measurements.
USEFUL FOR

This discussion is beneficial for high school students studying thermodynamics, educators teaching calculus and geometry, and anyone interested in practical applications of mathematical concepts to real-world diagrams.

TheAnt
Messages
19
Reaction score
1
The question is in the title. However my mathematical ability is limited as I am a high school student.

Thank you in advance
 
Science news on Phys.org
Many different methods . Post the diagram and tell us where it originates .
 
Cut out the area with a scissors and weigh it on a sensitive balance. Then cut out a known rectangular area of the paper and weigh it to calibrate the paper.
 
  • Like
Likes   Reactions: Buffu
Chestermiller said:
Cut out the area with a scissors and weigh it on a sensitive balance. Then cut out a known rectangular area of the paper and weigh it to calibrate the paper.
Thank you I will try this, I do not know if I have access to a sensitive enough balance.
 
Nidum said:
Many different methods . Post the diagram and tell us where it originates .
400px-Carnot_cycle_p-V_diagram.svg.png
 
You're a high school student, but some high school students have had calculus. Have you had integral calculus yet?
 
Trace the shape onto squared graph paper and count the squares. You'll find that most fractions of a square can readily be paired with another to form the equivalent of one whole square, then use your best estimate for the area of each of those remaining.

holly-1756.gif
 
Chestermiller said:
Have you had integral calculus yet?
And do you know the P-V equations for each "side" of the figure in your diagram?
 

Similar threads

Undergrad Understanding the Clausius-Clapeyron Formula: V_{l} and V_{g}
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Is There a Curve For a Material's Surface Area vs. UTS
  • · Replies 2 ·
Replies
2
Views
1K
High School Not sure about the magnetic flux (phi) depending on a cosine function
  • · Replies 9 ·
Replies
9
Views
2K
High School Knudsen Flow: High School Student Q&A
  • · Replies 4 ·
Replies
4
Views
2K
High School Help with science experiment magnets/force/acceleration/speed
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Mass measurement in a Penning trap
  • · Replies 0 ·
Replies
0
Views
985
Graduate Clausius clapeyrion equation Hfg
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What thermal cycle would describe the action of a candle carousel?
  • · Replies 4 ·
Replies
4
Views
799
How to make an Electrical Diagram with added Steinmetz Circuit for a Delta 3 phase motor?
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad How did Charles obtain his law when absolute temperature wasn't define
  • · Replies 3 ·
Replies
3
Views
2K