The temperature of an ideal gas undergoing adiabatic expansion varies with volume as T propto V- (3/4), then the value of (CP/CV) for the gas is

Question

The temperature of an ideal gas undergoing adiabatic expansion varies with volume as T propto V- (3/4), then the value of (CP/CV) for the gas is (A) (3/5) (B) (5/3) (C) (7/3) (D) (7/4)

Tardigrade Admin · Accepted Answer

Given, T propto V- 3/4⇒ TV3/4=Constant Comparing it with the relation for the adiabatic process we get TV&gamma; - 1=TV3/4⇒ &gamma; -1=(3/4)⇒ &gamma; =(7/4)

Q. The temperature of an ideal gas undergoing adiabatic expansion varies with volume as $T \propto V^{- \frac{3}{4}},$ then the value of $\frac{C _{P}}{C _{V}}$ for the gas is

$\frac{3}{5}$

$\frac{5}{3}$

$\frac{7}{3}$

$\frac{7}{4}$

Given,
$T \propto V^{- 3/4} \Rightarrow T V^{3/4} = C o n s t an t$
Comparing it with the relation for the adiabatic process we get
$T V^{γ - 1} = T V^{3/4} \Rightarrow γ - 1 = \frac{3}{4} \Rightarrow γ = \frac{7}{4}$

Q. The temperature of an ideal gas undergoing adiabatic expansion varies with volume as T∝V−43​, then the value of CV​CP​​ for the gas is

53​

35​

37​

47​