n our discussions of the heat capac es in class, we assumed a constant heat capa

Question

n our discussions of the heat capac es in class, we assumed a constant heat capacity. This is can be a poor assumption, particularly for gases. If you examine different books, you will find a wide variety of curve fits for the heat capacity of gases. The ideal gas heat capacity of oxygen, for example, is given by the following equations by different authors: a. Borgnakke and Sonntag CD 3 0.88 0.000 10 0.540 0.330 b. Felder and Rousseau 0.6076 10 8T2 2T3 29.10 10-3 1.158 10 ST 1.311 10 with T in C and Cp in kJ/mol K. c. Reid, Prausnitz and Poling: CO 28.11 3.680 10-6T 1.746 10-5T2 1.065 10-8T3 with T in K and cp in J/mol K d. Smith, Van Ness and Abbott: 3.639 0.506 10-3T 0.227 105T-2 with Tin K. All of these equations supposedly represent the "exact" values presented in ideal gas tables. Use each of heat capacity equations to find the change in specific enthalpy of oxygen going from 500 K to 1000 K and compare the predictions to the values in the ideal gas table (Table A.8 on page 764). Comment on the results

Explanation / Answer

(a)

Using first equation

Cp0 = 0.88 - 0.001 * theta + 0.54 * (theta)^2 - 0.33 * (theta)^3

For T = 500 K , theta = 500 / 1000 = 1/2 and for T = 1000 K , theta = 1000 / 1000 = 1

Cp0 for theta = 1 is

Cp0 = 0.88 - 0.0001 + 0.54 - 0.33 = 1.0899 kJ/kg-K

Cp0 for theta = 1/2 is

Cpo = 0.88 - 0.0001 * 0.5 + 0.54 * (0.5)^2 - 0.33 * (0.5)^3

Cpo = 0.97325 kJ/kg-K

Change in Cpo = 1.0899 - 0.97325 = 0.11665 kJ/kg-K

(b)

Using 2nd equation

Cpo = 29.10 x 10^-3 + 1.158 x 10^-5 * T - 0.6076 x 10^-8 * T^2 - 1.311 x 10^-12 T^3

For T = 500 K = 227 degreeC

Cpo = 0.0314 kJ/mol-K

For T = 1000 K = 727 degreeC

Cpo = 0.0338 kJ/mol-K

So, Change in Cpo = 0.0338 - 0.0314 = 0.0024 kJ/mol-K

(c) Using 3rd equation

Cpo = 28.11 - 3.680 x 10^-6 * T + 1.746 x 10^-5 * T^2 - 1.065 x 10^-8 * T^3

For T = 500 K

Cpo = 31.142 J/mol-K

For T = 1000 K

Cpo = 34.916 J/mol-K

so,

Change in Cpo = 3.774 J/mol-K

(d) Using 4th equation

Cpo / R = 3.639 + 0.506 x 10^-3 * T - 0.227 x 10^5 T^-2

At T = 500 K

Cpo / R = 3.8012

At T = 1000 K

Cpo / R = 4.1223

So,

Change in Cpo / R = 0.3211

Change in Cpo = 0.3211 * 8.314 J/mol-K = 2.670 J/mol-K

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