Question

The ratio Cp / Cv for a gas is 1.29. What is the degree of freedom of the molecules of this gas?

Answer 1

The degree of freedom of the molecules of this gas is f = 7

Explanation:

Give  γ = 1.29

For the molecules of gas  "γ" = Cp/Cv

                                               = 1 + 2/f

" f "is the freedom of degree.

 = 1 + 2/f = 1.29 = 9/7

2/f = 9/7 - 1

2/f = 2/7

f = 7

Thus the degree of freedom of the molecules of this gas is f = 7

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Answer 2

The degree of freedom of the molecules of this gas is 7.

in reality no gas can be free of more than 6 degrees.

Explanation:

Step 1:

For the gas of a molecules

The $\frac{C_p}{C_v}$ ratio is

$\gamma=\frac{c_{p}}{c_{v}}=1+\frac{2}{f}$

where

f = the degree of freedom.

Step 2:

given in the question γ=1.29

$1+\frac{2}{f}=1.29$

$1.29 can be written as \frac{9}{7}$

because $\frac{9}{7}$  is equal to 1.29

Step 3:

so

$\begin{aligned}&1+\frac{2}{f}=\frac{9}{7}\\&\frac{2}{f}=\frac{9}{7}-1\\&\frac{2}{f}=\frac{9-7}{7}\end{aligned}$

$\begin{aligned}&\frac{2}{f}=\frac{2}{7}\\&2 f=14\\&f=\frac{14}{2}\end{aligned}$

f=7  

The molecules of this gas thus have seven degrees of freedom.  

But in reality no gas can be free of more than 6 degrees.