Before you turn this problem in, make sure everything runs as expected. First, restart the kernel (in the menubar, select Kernel\(\rightarrow\)Restart) and then run all cells (in the menubar, select Cell\(\rightarrow\)Run All).

Make sure you fill in any place that says YOUR CODE HERE or “YOUR ANSWER HERE”, as well as your name and collaborators below:

From thermodynamics, the heat capacity is defined as \(C_p = \left(\frac{dH}{dT}\right)_P\). That means we can calculate the heat required to change the temperature of some material from the following integral:

\(H_2 - H_1 = Q = \int_{T_1}^{T_2} C_p(T) dT\)

In the range of 298-1200K, the heat capacity of CO₂ is given by a Shomate polynomial:

\(C_p(t) = A + B t + C t^2 + D t^3 + E/t^2\) with units of J/mol/K.

where \(t = T / 1000\), and \(T\) is the temperature in K. The constants in the equation are

	value
A	24.99735
B	55.18696
C	-33.69137
D	7.948387
E	-0.136638
F	-403.6075
G	228.2431
H	-393.5224

Use this information to compute the energy (Q in kJ/mol) required to raise the temperature of CO₂ from 300K to 600K. You should use scipy.integrate.quad to perform the integration.

The change in enthalpy (in kJ / mol) from standard state is

\(dH − dH_{298.15}= A t + B t^2/2 + C t^3/3 + D t^4/4 − E/t + F − H\)

again, \(t = T / 1000\).

Use this equation to compute the change in enthalpy when you increase the temperature from 300 K to 600 K. Hint: You should get the same answer as before.

When you are done, download a PDF and turn it in on Canvas. Make sure to save your notebook, then run this cell and click on the download link.

%run ~/f23-06623/f23.py
%pdf