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change in enthalpy in heating air from 250K to 1200 K three different ways.

change in enthalpy in heating air from 250K to 1200 K three different ways.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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When large temperature variations occur, specific heats of perfect gases vary considerably. Two techniques are employed to improve accuracy under these conditions. Most commonly, the specific heat data are curvefit as a function of temperature to permit integration over the desired temperature range. For air, we have integration over the desired temperature range. For air, we have: C, =27.345+0.1839 (T/1000)+0.89932 (T/1000) 10 MERGEFORMAT()) where C, is in J/g-mol K and T is in Deg. K. One technique is to use the given C, function to calculate an averaged specific heat over the desired temperature range: fc, dr T₂- 22\* MERGEFORMAT() A second technique involves an effective averaging by using C, values at the high temperature (C₁2) and low temperature (C₂1) extremes AH =C₁ (T₂-T.)- C₁ (T. -T.) 33\* MERGEFORMAT() where To is some reference temperature. Calculate the change in enthalpy in heating air from 250K to 1200 K three different ways. a) Using the average specific heat procedure shown in Eq. (2). b) Using the averaging scheme described in Eq. (3) with To = 298 K c) Using a constant C, corresponding to the value at 250K. Note: Use Eq. (1) to obtain C, values at temperature extremes. d) In combustion problems, AH is known and we wish to calculate T₂. Assuming the result in Eq. (1) is exactly correct, how would the procedures performed in Parts (b) and (c) compare with the exact solution? i.e., would these methods over or under predict T₂? e) Plot the variation of C, with temperature as indicated in Eq. (1) for temperatures between 250 and 1200K.
Transcribed Image Text:When large temperature variations occur, specific heats of perfect gases vary considerably. Two techniques are employed to improve accuracy under these conditions. Most commonly, the specific heat data are curvefit as a function of temperature to permit integration over the desired temperature range. For air, we have integration over the desired temperature range. For air, we have: C, =27.345+0.1839 (T/1000)+0.89932 (T/1000) 10 MERGEFORMAT()) where C, is in J/g-mol K and T is in Deg. K. One technique is to use the given C, function to calculate an averaged specific heat over the desired temperature range: fc, dr T₂- 22\* MERGEFORMAT() A second technique involves an effective averaging by using C, values at the high temperature (C₁2) and low temperature (C₂1) extremes AH =C₁ (T₂-T.)- C₁ (T. -T.) 33\* MERGEFORMAT() where To is some reference temperature. Calculate the change in enthalpy in heating air from 250K to 1200 K three different ways. a) Using the average specific heat procedure shown in Eq. (2). b) Using the averaging scheme described in Eq. (3) with To = 298 K c) Using a constant C, corresponding to the value at 250K. Note: Use Eq. (1) to obtain C, values at temperature extremes. d) In combustion problems, AH is known and we wish to calculate T₂. Assuming the result in Eq. (1) is exactly correct, how would the procedures performed in Parts (b) and (c) compare with the exact solution? i.e., would these methods over or under predict T₂? e) Plot the variation of C, with temperature as indicated in Eq. (1) for temperatures between 250 and 1200K.
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