Question

calculate the adiabatic ratio for a polyatomic gas have 2 vibrational degrees of freedom​

Answer 1

Adiabatic ratio (or adiabatic index) for POLYATOMIC GAS:

• First of all , this is a ratio of C_(p) and C_(v), where signs have there usual meaning.

When degrees of freedom is 2 :

$\rm C_{v} = \dfrac{f}{2} \times R$

$\implies \rm C_{v} = \dfrac{2}{2} \times R$

$\implies \rm C_{v} = R$

Now, we know that :

$\implies \rm C_{p} - C_{v} = R$

$\implies \rm C_{p} = C_{v} + R$

$\implies \rm C_{p} = 2R$

Now, required ratio :

$\rm \therefore \: \gamma = \dfrac{C_{p}}{C_{v}}$

$\rm \implies \: \gamma = \dfrac{2R}{R}$

$\rm \implies \: \gamma = 2$

So, adiabatic index is 2 .

Answer 2

Explanation:

First of all , this is a ratio of C_(p) and C_(v), where signs have there usual meaning.

When degrees of freedom is 2 :

\rm C_{v} = \dfrac{f}{2} \times RC

v

=

2

f

×R

\implies \rm C_{v} = \dfrac{2}{2} \times R⟹C

v

=

2

2

×R

\implies \rm C_{v} = R⟹C

v

=R

Now, we know that :

\implies \rm C_{p} - C_{v} = R⟹C

p

−C

v

=R

\implies \rm C_{p} = C_{v} + R⟹C

p

=C

v

+R

\implies \rm C_{p} = 2R⟹C

p

=2R

Now, required ratio :

\rm \therefore \: \gamma = \dfrac{C_{p}}{C_{v}}∴γ=

C

v

C

p

\rm \implies \: \gamma = \dfrac{2R}{R}⟹γ=

R

2R

\rm \implies \: \gamma = 2⟹γ=2