n moles of an ideal triatomic linear gas undergoes a process in which the temperature changes with volume as `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

D

Explanation

At normal temperature `C_(v) = (f)/(2)R = (5)/(2)R`
At any temperature `C_(p) - C_(v) = ((f)/(2)+1) - (f)/(2)R = R` from process `" " T = k_(1)V^(2)` and
Ideal gas equation `PV= nRT`
we have `PV^(-1)` = constant `implies x = -1`
`implies C =C_(v) + (R)/(1-x) = C_(v) + (R)/(1+1) = C_(v) + (R)/(2)`
At normal temperature
` C = (5)/(2)R + (R)/(2) = 3R`