Question 726: Thermodynamics & KTG

Question

The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$, in terms of degrees of freedom ( n ) is

Accepted Answer

The ratio of the specific heats, denoted as $\frac{C_p}{C_v} = \gamma$, can be expressed in terms of the degrees of freedom ($ n $) of a gas.
We start with the relationship for the specific heat at constant volume, given by:
$ C_v = n 	imes \frac{R}{2} $
Using the relation $ C_p - C_v = R $, we can solve for $ C_p $:
$ C_p = C_v + R = \frac{n R}{2} + R = \left(\frac{n}{2} + 1ight) R  $
Now, the ratio of the specific heats $\gamma$ is:
$ \frac{C_p}{C_v} = \frac{\left(\frac{n}{2} + 1ight) R}{\frac{n R}{2}} = \left(1 + \frac{2}{n}ight) $

Answer

$\left(1+\frac{1}{n}\right)$

Answer

$\left(1+\frac{2}{n}\right)$

Answer

$\left(1+\frac{\mathrm{n}}{3}\right)$

Answer

$\left(1+\frac{\mathrm{n}}{2}\right)$

Thermodynamics & KTG

The ratio of the specific heats \frac{C_p}{C_v}=\gamma, in terms of degrees of freedom ( n ) is

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