Isentropic Compression or Expansion
https://www.grc.nasa.gov/www/k-12/airplane/compexp.html13.05.2021 · Since there is no heat transferred into the cylinder and no other losses, the change in entropy is zero. Then the equation becomes: cp ln (T2 / T1) = R ln (p2 / p1) We divide both sides by "cp" and take the exponential function of both sides (this "un-does" the logarithms). T2 / T1 = (p2 / p1) ^ (R / cp) where the symbol "^" denotes an exponent.
Heat equation - Wikipedia
https://en.wikipedia.org/wiki/Heat_equationFor heat flow, the heat equation follows from the physical laws of conduction of heat and conservation of energy (Cannon 1984). By Fourier's law for an isotropic medium, the rate of flow of heat energy per unit area through a surface is proportional to the negative temperature gradient across it: where is the thermal conductivity of the material, is the temperature, and is a vectorfield that repres…