#!/usr/bin/env python
# coding: utf-8

# # Homework 12

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import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')


# ## Problem 1
# 
# Read the posted notes for variables, dictionaries, and tuples. State if you did this.

# 

# ## Problem 2
# 
# If a dictionary has a value that is an array, we can access elements of the array as follows. (First we make the dictionary, then we access an array element.)
# 
# ```python
# a = {
#     'CO2':np.array([0.1, 2.2, 33.3]),
#     'H2O':np.array([0.2, 3.8, 44.4]),  # useful optional end comma 
#     }                                  # makes each line the same
# a['CO2'][1]    # --> 2.2
# ```
# 
# That is ```a['CO2']``` is the array, and the following ```[1]``` accesses the given element.
# 
# The heat capacity of a species $i$ is given by
# $$c_{p,i}(T) = R_g(a_{0,i} + a_{1,i}T + a_{2,i}T^2 + a_{3,i}T^3 + a_{4,i}T^4)$$ 
# 
# The following species data are given:
# 
# 
# | Species | $a_0$           | $a_1$             | $a_2$            | $a_3$             | $a_4$             |
# |---------|-----------------|-------------------|------------------|-------------------|-------------------|
# | CO2     | 2.356773520E+00 |   8.984596770E-03 | -7.123562690E-06 |   2.459190220E-09 |  -1.436995480E-13 |
# | H2O     | 4.198640560E+00 |  -2.036434100E-03 |  6.520402110E-06 |  -5.487970620E-09 |   1.771978170E-12 |
# | O2      | 3.782456360E+00 |  -2.996734160E-03 |  9.847302010E-06 |  -9.681295090E-09 |   3.243728370E-12 |
# | N2      | 3.298677000E+00 |   1.408240400E-03 | -3.963222000E-06 |   5.641515000E-09 |  -2.444854000E-12 |
# | CH4     | 5.149876130E+00 |  -1.367097880E-02 |  4.918005990E-05 |  -4.847430260E-08 |   1.666939560E-11 |
# 
# * Write a dictionary containing this data.
# 

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# ## Problem 2
# 
# * Refer to Problem 1. Now write a function called ```cp``` that takes two arguments: a string that gives the name of the species, and the temperature.
#     * The function should return the heat capacity of the given species at the given temperature. 
#     

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# ## Problem 3
# * Refer to Problems 1 and 2
# * A mixture heat capacity can be found from 
# $$c_p(x,T) = \sum_i x_ic_{p,i}(T),$$
# where $x_i$ are species mole fractions.
# 
# * Write a function called ```cp_mix``` that takes two arguments: a dictionary containing the names and mole fractions of species, and the temperature.
#     * This function should evaluate the mixture $c_p$ using a loop that calls the function you wrote Problem 2.
#     

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# ## Problem 4
# * Refer to Problems 1, 2, and 3
# * Use the function ```cp_mix``` to evaluate the mixture heat capacity at T=900 K, for the following mixture (corresponding to a stoichiometric mixture of methane and air (CH4 + 2O2 + 7.52 N2):
#     * $x_{CH_4} = 0.095$,
#     * $x_{O2} = 0.19$,
#     * $x_{N2} = 0.715$.

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# ## Problem 5
# * Refer to the above problems
# * Create an array of temperatures from 300 to 1000 K with steps of 2 K.
# * Use your cp_mix function to find an array of cp values at each temperature for the same mixture as in Problem 4.
# * Plot $c_{p,mix}$ versus $T$.

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