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

Answer

A, B, C

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)` 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`