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; infinite.

Programming language

Notation of computer programs; is source code that is translated to assembly code.

Integer

Positive or negative; no decimal.

Float

Positive or negative; has decimal.

Bool

Represents 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; represented as []

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; represented as (); defined variables

Sets

Nonredundant group of elements of any data set; no indices; membership testing

Dictionary

Table that associates a key with a value; no order but does not repeat keys.

What is this

x = ['x':5, 'a':True]:Dictionary.

Functions

Callable set of operations.

Classes

Defines attributes and methods/structure of variables and functions.

Object-oriented programming

Abstraction of contained elements.

Z-score

How many standard deviations from the mean; standardized.

What means that sample has estimated std

Need to use n-1 in std because already have uncertainty in the mean.

Cumulative distribution function

Probability that X will take on a random value x; used 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 the mean; patterns of variance.

What does it mean for a data system to follow normal distribution

Means that behavior of system is consistent with expectations of independent random behavior.

Gay-Lussac’s Law

Pressure proportional to temperature; P~kT.

Boyle-Mariotte Law

Pressure inversely proportional to volume (i.e., 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 because T is related to KE and 1/2mv^2; also rms velocity is proportional to the square root of temperature.

Maxwell–Boltzmann distribution

Probability density function of speed of ideal gases; chi distribution with three degrees of freedom; most move close to normal (0) but a few move faster.