First slide

Specific heat and degrees of freedom

Question

Considering the gases to be ideal, the value of $γ = \frac{C_{P}}{C_{V}}$ for a gaseous mixture consisting of = 3 moles of carbon dioxide and 2 moles of oxygen will be $(γ_{O_{2}} = 1 .4, γ_{{CO}_{2}} = 1 .3)$

Moderate

A

1.37
B

1.34
C

1.55
D

1.63

Solution

$γ_{mix} = \frac{\frac{μ_{1} γ_{1}}{γ_{1} - 1} + \frac{μ_{2} γ_{2}}{γ_{2} - 1}}{\frac{μ_{1}}{γ_{1} - 1} + \frac{μ_{2}}{γ_{2} - 1}} = \frac{\frac{3 \times 1 .3}{(1 .3 - 1)} + \frac{2 \times 1 .4}{(1 .4 - 1)}}{\frac{3}{(1 .3 - 1)} + \frac{2}{(1 .4 - 1)}} = 1 .33$

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