The molar specific heats of an ideal gas at constant pressure and volume are denoted by CP and CV, respectively. If γ = (CP/ CV) and R is the universal gas constant, then CV is equal to :

Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by CP and CV, respectively. If &gamma; = (CP/ CV) and R is the universal gas constant, then CV is equal to : (A) &gamma; R (B)  (1 + &gamma;/1 - &gamma;) (C)  (R/(&gamma; - 1))  (D)  (( &gamma; - 1)/R)

Tardigrade Admin · Accepted Answer

Using CP-CV=R ⇒ CV((CP/CV)-1)=R (&gamma;-1)=(R/CV) (∵ (Cp/CV)=&gamma;) or CV=(R/(&gamma;-1))

Q. The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P}$ and $C_{V}$ , respectively. If $γ = \frac{C _{P}}{C _{V}}$ and $R$ is the universal gas constant, then $C_{V}$ is equal to :

$γ R$

$\frac{1 + γ}{1 - γ}$

$\frac{R}{( γ - 1 )}$

$\frac{( γ - 1 )}{R}$

Using
$C_{P} - C_{V} = R$
$\Rightarrow C_{V} (\frac{C _{P}}{C _{V}} - 1) = R$
$(γ - 1) = \frac{R}{C _{V}}$
$(∵ \frac{C _{p}}{C _{V}} = γ)$
or $C_{V} = \frac{R}{( γ - 1 )}$

Q. The molar specific heats of an ideal gas at constant pressure and volume are denoted by CP​ and CV​, respectively. If γ=CV​CP​​ and R is the universal gas constant, then CV​ is equal to :

γR

1−γ1+γ​

(γ−1)R​

R(γ−1)​