Tutorial 6 - 2010

Due date(s):	28 October 2010
(PDF)	Tutorial questions
Other instructions	Hand-in at class.

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.. |m3| replace:: m\ :sup:`3` .. highlight:: python

.. rubric:: Tutorial objectives: Lagrange and Newton interpolation; due 28 October.

Question 1 [2]

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Use the heat capacity data in the course slides (slide 5) at :math:`T = [300, 500, 900]` K, with corresponding heat capacities :math:`C_p = [29.85, 30.51, 33.42] \rm J\ mol^{-1}\ K^{-1}`

1. . Construct the Lagrange interpolating polynomial of order 2 that passes through all three data points. There is no need to simplify the polynomial.
2. . Using this polynomial, compute (i.e. predict) the estimated heat capacity at :math:`T = 400` K and :math:`T = 800` K. Are the predictions reasonable?
3. . Create a computer plot that shows your polynomial, over the range :math:`T \in [300, 1600]` K. Superimpose on this plot the 14 data points from slide 5 in the course notes.

Where is the greatest prediction error in your polynomial? Is this expected?

1. . If you were to construct the Newton interpolating polynomial and estimate the heat capacities at :math:`T = 400` K and :math:`T = 800` K, what answer would you get? Explain.

Question 2 [1]

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The heat of reaction for a specific reaction depends on temperature as follows:

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math:`T \rm[^\circ C]` -250 -200 -100 0 100 300

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math:`\Delta H_R \rm[J\ mol^{-1}\ K^{-1}]` 160.0 318.0 699.0 870.0 941.0 1040

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1. . Express :math:`\Delta H_R` as a 5th-order polynomial using the Newton form of the interpolating polynomials. Report your intermediate results in a chart, as shown in the course material.
2. . Estimate :math:`\Delta H_R(T=200 \rm ^\circ C)` and :math:`\Delta H_R(T=400 \rm ^\circ C)` using the Newton polynomials. Comment on the results.

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