If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., (CP/CV)=γ, the respective values of CP and CV are

Question

If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., (CP/CV)=&gamma;, the respective values of CP and CV are (A) ( R /&gamma;-1), (&gamma; R /&gamma;-1) (B) (&gamma; R /&gamma;-1), ( R /&gamma;-1) (C) (&gamma;-1/&gamma; R ), (&gamma;-1/ R ) (D) (&gamma;-1/ R ), (&gamma;-1/&gamma; R )

Tardigrade Admin · Accepted Answer

(CP/CV)=&gamma; and CP-CV=R CP-(CP/&gamma;)=R ⇒ CP((&gamma;-1/&gamma;))=R ⇒ CP=(&gamma; R/&gamma;-1) &gamma; CV-CV=R ⇒ CV(&gamma;-1)=R ⇒ CV=(R/&gamma;-1)

Q. If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., $\frac{C _{P}}{C _{V}} = γ$ , the respective values of $C_{P}$ and $C_{V}$ are

$\frac{R}{γ - 1}, \frac{γ R}{γ - 1}$

$\frac{γ R}{γ - 1}, \frac{R}{γ - 1}$

$\frac{γ - 1}{γ R}, \frac{γ - 1}{R}$

$\frac{γ - 1}{R}, \frac{γ - 1}{γ R}$

$\frac{C _{P}}{C _{V}} = γ$ and $C_{P} - C_{V} = R$
$C_{P} - \frac{C _{P}}{γ} = R$
$\Rightarrow C_{P} (\frac{γ - 1}{γ}) = R \Rightarrow C_{P} = \frac{γ R}{γ - 1}$
$γ C_{V} - C_{V} = R$
$\Rightarrow C_{V} (γ - 1) = R \Rightarrow C_{V} = \frac{R}{γ - 1}$

Q. If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., CV​CP​​=γ, the respective values of CP​ and CV​ are

γ−1R​,γ−1γR​

γ−1γR​,γ−1R​

γRγ−1​,Rγ−1​

Rγ−1​,γRγ−1​