Adiabatic Compressor: Ideal Gas Temperature Change

[runningman19]

Homework Statement

A mixture of hydrogen, carbon monoxide and carbon dioxide is being fed to a compressor at 2.0 bar and 25 C. The overall flow rate is 17.47 SCMS and its composition is 73.5 mol% H₂, 13.7 mol% CO and the balance CO₂ The compressor operates adiabatically and reversibly with a discharge pressure of 6.0 bar. Assume ideal gas mixture behavior

1. Calculate the compressor discharge temperature in C

You may assume that the specific heat capacities of the gasses at constant pressure are not a function of temperature and that they can be calculated using the following information. For diatomic (H₂, CO): C_p = 7/2*R; for polyatomic CO₂: C_p = 4*R where R = 8.314 J/mol K

Homework Equations

(1)$$\Delta U = -P\Delta V$$
(2)$$\frac{T_1}{T_2} = (\frac{P_2}{P_1})^{R/C_p}$$

The Attempt at a Solution

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I have not started any calculations yet. The biggest problem I am having is figuring out how having a mixture of diatomic and polyatomic molecules would affect temperature change. For example, if only diatomic compounds were present (e.g. H₂ and CO), I could simply use equation 2 to calculate final temperature. How would I solve for final temperature with a combination of diatomic and polyatomic compounds?

 

[Chestermiller]

How is the heat capacity of an ideal gas mixture related to the heat capacity of each of its components?

 

[runningman19]

How is the heat capacity of an ideal gas mixture related to the heat capacity of each of its components?

$$C_{p(mixture)}=\sum C_{p(i)}x_i$$

Thank You.