Question

Calculate g (ratio of $C_{p}and{C}_y$) for triatomic linear gas at high temperature. Assume that the contriburtion of vibrationa degree of freedom is $75\%$:

• A. $1.222$
• B. $1.121$
• C. $1.18$
• D. $1.33$

Answer 1

Answer: (A)

$1.222$

For Triatomic molecule $N=3$

Degree of freedom $=2N=9$

$3\to$ Traslation degree of freespm

For linear, $2\to$ Rotatuional degree of freedom

$9-(3+2)=4\to$ Vibrational degree of freedom

$U=3\times \frac{1}{2}kT+2\times \frac{1}{2}kT+4\times \frac{75}{100}kT$

as vibrational contribution only $75\%$

$Udfrac32kT+kT+3kT=\frac{11}{2}kT$

$C_v=\frac{dU}{dT}=\frac{11}{2}k$ ot for $1$ mole $\frac{11}{2}R$

as for idela gas

$C_p-C_v=R$

$C_p=C_v+R=\frac{11}{2}R+R=\frac{13}{2}R$

$g=\frac{c_p}{c_v}=\frac{13}{2}R\times \frac{2}{11R}=1.18$

Thus, the ratio of $C_p$ and $C_v$ is $1.18$