What Is Adiabatic Change and How Does It Relate to the Laplacian?

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    Adiabatic Change
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SUMMARY

Adiabatic change is defined by the equation p ⁢ V γ = const, which describes a thermodynamic process where no heat is exchanged. The discussion elaborates on the relationship between adiabatic change and the Laplacian operator in four-dimensional space, incorporating time as an additional dimension. The standard Laplacian in rectilinear coordinates is expressed as del2 E = d2E/dx2 + d2E/dy2 + d2E/dz2 = 0, and when time is included, it transforms to box2 E = d2E/dx2 + d2E/dy2 + d2E/dz2 - 1/c2 d2E/dt2 = 0. This formulation highlights the complexity of analyzing physical phenomena in four-dimensional spacetime.

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  • Familiarity with the Laplacian operator in mathematics
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mikeasabsa
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what is it i cannot under stand this or other equation(Adiabatic Change p ⁢ V γ = const )
 
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I think it is a 4 dimensional Laplacian (x, y, z, and time).
 
Hi Mike
The standard Laplacian in rectilinear coordinates is
del2 E = d2E/dx2 + d2E/dy2 + d2E/dy2 = 0

We add to it another term: -1/c2 d2E/dt2

to get

box2 E = d2E/dx2 + d2E/dy2 + d2E/dy2 -1/c2 d2E/dt2= 0

So the square box is the Laplacian in 4 coordinates: x, y, z, and t
 
Last edited:

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