mamah1.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
__author__ = "Max Kovgan <kovganm@gmail.com>,"
import sys

if sys.version_info <= (2, 6, 0):
    print "This script requires python v2.6 and up"
    sys.exit(1)
import math
from openuhw import OpenUHWSolver, OpenUHWResult

AVOGADRO_CONSTANT = float(6.022141E23) # entities/mol
PI = math.pi

mamah1 = OpenUHWSolver()


def box_volume(l, w=None, h=None):
    """
    returns l*w*h.
    l length
    w width
    h height

    """
    length = l
    width = w if w else l
    height = h if h else l
    return length * width * height

# def cube_volume(d):
#    return box_volume(d)

def sphere_volume(r):
    return ((4.0 / 3.0) * PI) * box_volume(r)


def ex_1():
    """
    hw1 ex1
    """
    result = OpenUHWResult(title=u"ex1")
    a = float(1.0E6)
    b = float(5.0E-3)
    c = float(0.5E2)
    result.answers.append(
        dict(
            descr=u"ABC",
            result=a * b * c,
        )
    )
    result.answers.append(
        dict(
            descr=u"AC^(-2)",
            result=(a / (c * c)),
        )
    )
    return result


def ex_2():
    result = OpenUHWResult(title=u"ex2")
    r_atom = float(1.0E-10)
    r_earth = float(6.37E6)
    v_atom = box_volume(r_atom) ## annoying assumption
    v_earth = sphere_volume(r_earth)
    ratio = v_earth / v_atom
    result.answers.append(
        dict(
            descr=u"V(earth)/'V'(atom)",
            result=ratio,
        )
    )
    return result


def ex_3():
    result = OpenUHWResult(title=u"ex3")
    ## box a,b,c
    a = float(9.7E-2) # m
    b = float(5.3E-2) # m
    c = float(4.4E-2) # m
    err = float(0.5E-3) # m
    vol_box = box_volume(a, w=b, h=c)
    ## minimal box
    a_min = a - err
    b_min = b - err
    c_min = c - err
    ## maximal box
    a_max = a + err
    b_max = b + err
    c_max = c + err
    ## compare:
    vol_min = box_volume(a_min, b_min, c_min)
    vol_max = box_volume(a_max, b_max, c_max)
    vol_err = (vol_max - vol_min) / 2
    result.answers.append(
        dict(
            descr=u"V(box)±err",
            result=u"{vol_box}m^3±{vol_err}m^3".format(**locals()),
        )
    )
    return result


def ex_4():
    result = OpenUHWResult(title=u"ex4")
    density_hg = float(13.58) # in g/cm^3
    atomic_mass_hg = float(200.59) # in AMU i.e. g/mol

    ## how many atoms of Hg are there in 1 cm^3?
    vol = float(1) # in cm^3
    mass_hg = vol * density_hg ## grams
    molar_mass = mass_hg / atomic_mass_hg # mols
    atoms_count = molar_mass * AVOGADRO_CONSTANT
    result.answers.append(
        dict(
            descr=u"atoms_count(hg, vol=1 cm^3)",
            result=atoms_count,
        )
    )
    molar_mass = 1 # moles
    mass_hg = molar_mass * atomic_mass_hg # grams
    vol = mass_hg / density_hg
    result.answers.append(
        dict(
            descr=u"volume(hg, 1 mol)",
            result=vol,
        )
    )
    return result


def ex_5():
    result = OpenUHWResult(title=u"ex5")
    sound_speed_air = float(333.33) ## m/sec
    light_speed_air = float(3.0E8) ## m/sec

    ## how many orders of magnitude is speed of light higher than speed of sound?
    ### ans: numb. of orders of magnitude := log10 ( ratio )
    ### question is: how many WHOLE orders of magnitude ? it's floor rounding!
    result.answers.append(
        dict(
            descr=u"orders_of_mag(light,sound)",
            # result=math.log10(light_speed_air/sound_speed_air), ## the exact is 5.99 :) so it's 5!
            result=math.floor(math.log10(light_speed_air / sound_speed_air)),
        )
    )
    return result


def ex_6():
    result = OpenUHWResult(title=u"ex6")
    ## work in given units:
    density = float(1.55E-3) # in g/cm^-3
    density_per_litre = float(2.22E22) # atoms
    density_per_cubic_m = density_per_litre * float(1.0E3) # atoms
    moa_kg = density_per_cubic_m * density # kg
    ### convert to SI:
    kg2amu_coefficient = float(1.660538921E-27)
    # mass_of_an_atom = mass_of_an_atom_in_kg * float(1.0E-3)
    moa  = moa_kg
    ### hence:
    amu = moa / kg2amu_coefficient
    ## how many orders of magnitude is speed of light higher than speed of sound?
    result.answers.append(
        dict(
            descr=u"AMU(gas)",
            result=u"{}".format(str(amu)),
        )
    )
    return result


# def ex_7():
#     result = OpenUHWResult(title=u"ex7")
#     ## work in given units:
#     isotopes_data = [
#         dict(mass=float(23.985), probability=float(0.79), ),
#         dict(mass=float(24.9858), probability=None, ),
#         dict(mass=float(25.9826), probability=None, ),
#     ]
#     # iso_1_probability = float(0.79)
#     std_mass_in_amu = float(24.305)
#
#     result.answers.append(
#         dict(
#             descr=u"P(max(mass, {isotopes}))",
#             result=u"{}".format(str(amu)),
#         )
#     )
#     return result

solvers_list = [
    ex_1,
    ex_2,
    ex_3,
    ex_4,
    ex_5,
    ex_6,
]


[mamah1.add_solver(s) for s in solvers_list]

mamah1.solve(print_solution=True)