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Notes on the proper way to derive the equilibrium constant. Relevant for high school and university chemistry education.
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Proof of Small Gain Theorem
A Geometrical Proof of the Constant of Time By: Joseph H. Kang Proof: Assumptions: •
Given a circle that represents the Universe with endpoints on circumference o (+∞, -∞) or (lim 𝑠𝑝𝑎𝑐𝑒, lim 𝑠𝑝𝑎𝑐𝑒) or ∑Space
•
Given the circumference of any circle is 2πr o Accordingly, half the diameter of any circle is πr Given the diameter of a Circle is 2r And accordingly, Distance s = vt c = speed of light (3 x 108 km/s) I = the speed of time
• • • •
−∞
+∞
For energy to travel in time from (lim 𝑠𝑝𝑎𝑐𝑒, lim 𝑠𝑝𝑎𝑐𝑒): −∞
+∞
Δt = 2r/c (change in time to travel is the distance divided by speed of light)
For time to travel in time from (lim 𝑠𝑝𝑎𝑐𝑒, lim 𝑠𝑝𝑎𝑐𝑒): −∞
+∞
Δt = πr/I (the change in time to travel is the distance πR divided by the speed of time)
After setting equal terms to cancel out: Vt Vt
=
πr c 2𝑟 𝐼
The following relationship then occurs: 2r/C = πr/I