ME501HW4SolnF2011

# ME501HW4SolnF2011 - 1 ME 501 Homework#4 Due Monday November...

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1 ME 501 Homework #4 Due Monday, November 7, 2011 Prof. Lucht (E-mail address: 1. NML, Problem 2.5.

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4 2. NML, Problem 2.13.
5 3. NML, Problem 4.12

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7 4. Calculate the entropy, enthalpy, and constant pressure specific heat for carbon monoxide (CO) at 1000 K, 2000 K, and 3000 K for a pressure of 100 kPa. You can use either the semi-rigorous diatomic model in the book or write a short computer program to calculate the entropy, enthalpy, and constant pressure specific heat at these temperatures. The following spectroscopic data is from Mantz et al., J. Mol. Spectrosc. Vol. 57, pp. 155-159 (1975): Table 1 values are to be used with the following equation: For CO:

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8      ,v v exp jin t e Bj int j j TGF J hc k Zg T      The summation index in the internal partition function expression implies a summation over electronic implies a summation over the indices , v , and J . For CO, only the ground 1 is populated even at 3000 K and higher electronic levels ( 3 at 46,687 cm -1 is the next lowest level) will be ignored. Therefore we can write   v t GF J  and we need only sum over v and J . For CO, the number distribution over internal energy levels is given by , exp 21 t j int j hc k N Ng ZT gJ The contribution to assembly properties for the internal modes is given by ,, v v, v, exp int int int j int j j int j jj Av jJ J int J uhe N N h c hc k J Nh c Jg    where we calculate the properties per kmol by setting 26 6.022142 10 Av NN  . The contribution to the entropy is given by ln int int Av B int u sN k Z T The contribution to the specific heat is given by 2 v, , v 2 2 v v, v, exp v, v, exp int Av B int p int J J int P Av B J J int hc k J hc k J hN k cc g TZ T T hc k J hc k J Nk g T        
9 The translational contributions to the properties are given by , 3/2 5/2 2 ,, 55 22 2 ln ln ln tr Av B P tr Av B CO tr Av B B tr int PP t rP i n t tr int hN k T c N k m sN k T P k h hh h cc c ss s              I wrote a short Fortran program to calculate these properties as a function of temperature, including 20 vibrational levels and 300 rotational levels in the calculation. The results are shown below, along with table values from Laurendeau, Appendix E: Temp (K) calc h table h % error calc s table s % error , Pca lc c , P table c % error 298.15 0.00000 0.00000 0.0000 197.660 197.653 0.00384 29.1408 29.1420 - 0.00411 500.00 5930.59

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ME501HW4SolnF2011 - 1 ME 501 Homework#4 Due Monday November...

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