The animated plot clearly demonstrates the core distinction between thermodynamic properties: as the system's volume increases across the visualized range, intensive properties like Density ( $\rho$ ) and Specific Heat Capacity ( $c_V$ ) remain absolutely constant, confirming they are independent of the system's size and fixed characteristics of the air's state. Conversely, the extensive properties, specifically Mass ( $M$ ) and Total Heat Capacity ( $C_V$ ), are shown to increase linearly in direct proportion to the volume, confirming that extensive properties are additive and scale directly with the size of the system, mathematically validating the integral relationship $C_V=\int\left(\rho \cdot c_V\right) d V$.

🎬Narrated Video


https://youtu.be/-ujgd57IEpk


🏗️Structural clarification of Condensed Notes

block-beta
columns 5
CC["Criss-Cross"]:5

%% Condensed Notes

CN["Condensed Notes"]:5
RF["Relevant File"]:5
NV["Narrated Video"]:4 VO["Voice-over"] 
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") PO("Polyptych")

%% Proof and Derivation

PD["Proof and Derivation"]:5
AF("Derivation Sheet"):5
NV2["Narrated Video"]:4 VO2["Voice-over"]
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo") PO2("Polyptych")

classDef color_1 fill:#8e562f,stroke:#8e562f,color:#fff
class CC color_1

classDef color_2 fill:#14626e,stroke:#14626e,color:#fff
class CN color_2
class RF color_2

classDef color_3 fill:#1e81b0,stroke:#1e81b0,color:#fff
class NV color_3
class PA color_3
class AA color_3
class KT color_3
class ID color_3

classDef color_4 fill:#47a291,stroke:#47a291,color:#fff
class VO color_4
class PO color_4

%% Proof and Derivation

classDef color_5 fill:#307834,stroke:#307834,color:#307834
class PD color_5
class AF color_5

classDef color_6 fill:#38b01e,stroke:#38b01e,color:#38b01e
class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
class ID2 color_6

classDef color_7 fill:#47a291,stroke:#47a291,color:#47a291
class VO2 color_7
class PO2 color_7

🗒️Downloadable Files - Recursive updates



<aside> <img src="/icons/report_pink.svg" alt="/icons/report_pink.svg" width="40px" />

Copyright Notice

All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]

© 2025 Sayako Dean

</aside>