Abstraction + Python + Ideal Gas Laws

abstraction→organize system by structuring complex details into less complicated levels; macroscopic properties

ideal gas→random moving point particles; not subject to intermolecular interactions or energy exchange; no volume; infinate

programming language→notation of computer programs; is source code that is translated to assembly code

integer→pos or neg; no decimal

float→pos or neg; has decimal

bool→false or true

strings→contain characters as elements

lists→group of elements of any data type ordered based on index; start index at 0; can append; []

list x = [3, 0.5, False], what is x[2]→False

numpy→common library for numerical operations in python

tuples→lists that cannot be altered; ()

sets→nonredundant group of elements of any data set; no indecies

dictionary→table; associates a key with a value; no order but not repeat key

what is this: x = [‘x’:5, ‘a’: True]→dictionary

functions→callable set of operations

classes→defines attributes and methods/structure of variables and function

object-oriented programming→abstraction of contained elements

z-score→how many std deviations from mean; standardized

what means that sample has estimated std→need to use n-1 in std b/c already have uncertainty in the mean

cumulative distribution function→probability that X will take on a random value x; ex. use to show most probable z-score is -1 to 1

chi distribution→continuous probability distribution over non-negative numbers; distribution of positive square root of squared distance between Gaussian variable and origin; 

why is temperature constant in simulation→lack of interparticle interactions so nowhere to lose energy

normal distribution→shows how a data set converges; data clusters symmetrically around mean; patterns of variance

what does it mean for a data system to follow normal distribution→means that behavior of system is consistant with expectations of independent random behavior

Gay-Lussac’s Law→pressure proportional to temperature; P~kT

Boyle-Mariotte Law→pressure inversly proportional to volume (ie exponential decrease); P~1/V

Charles’s Law→volume proportional to temperature; V~T

Avogadro’s Law→pressure proportional to number of particles; P~n so V~n

Ideal Gas Law→PV=nRT

pressure + velocity relationship→quadratic; P~v^2 b/c T related to KE and 1/2mv^2; also rms velocty is proportional to square root of temperature

Maxwell–Boltzmann distribution→probability density function of speed of ideal gases; chi distribution with three degrees of freedom (b/c 2D velocity vector); each component of velocity vector is normally distributed so when calculate speed (pythagorean of velocity) is same formula to look at chi distribution; most move close to normal (0) but a few move faster