n moles of an ideal triatomic linear gas undergoes a process in which the temperature changes with volume as 'T'=` K_(1)`` V^(2)` where `k_(1)` is a constant. Choose incorrect alternative.

Options

A. At normal temperature `C_(v)=(5)/(2)R`
B. At any temperature `C_(p)-C_(v)=R`
C. At normal temperature molar heat capacity C=3R
D. At any temperature molar heat capacity C=3R

Answer

C

Explanation

At normal temperature `C_(v)=(f)/(2)R=(5)/(2)R`, At any
temperature `C_(v)-C_(v)=((f)/(2)+1)-(f)/(2)r=R`
from process `T=K_(1)V^(2) &` ideal gas equation PV `=nRT`
we have `PV^(-1)=` constant `rArr x=-1`
`rArr C=C_(v)+(R)/(1-x)=C_(v)+(R)/(1+1)=C_(v)+(R)/(2)`
At normal temperature `C=(5)/(2)R+(5)/(2)=3R`