First slide

Specific heat and degrees of freedom

Question

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is

Easy

A

11
B

15
C

13
D

20

Solution

oxygen bonds are rigid $\Rightarrow$ no vibrational degrees of freedom.
$U = n_{1} C_{v 1} T + n_{2} C_{v 2} T \Rightarrow U = 3 (\frac{5}{2} R T) + 5 (\frac{3}{2} R T) = 15 R T$

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