An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity Cremains constant. If during this process the relation of pressure P and volume V is given by PVn = constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) :

Question

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity Cremains constant. If during this process the relation of pressure P and volume V is given by PVn = constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) : (A) n = (CP/CV)  (B) n = (C - CP/C - CV)  (C) n = (CP - C /C - CV)  (D) n = (C - CV/C - CP)

Tardigrade Admin · Accepted Answer

C = CV + (R/1 - η) ⇒ 1 - n = (R/C -CV) n = 1 - (R/ C - CV) = (C - (CV + R)/C - CV) = (C-CP/C - CV)

$n = \frac{C _{P}}{C _{V}}$

$n = \frac{C - C _{P}}{C - C _{V}}$

$n = \frac{C _{P} - C}{C - C _{V}}$

$n = \frac{C - C _{V}}{C - C _{P}}$

$C = C_{V} + \frac{R}{1 - η}$
$\Rightarrow 1 - n = \frac{R}{C - C _{V}}$
$n = 1 - \frac{R}{C - C _{V}} = \frac{C - ( C _{V} + R )}{C - C _{V}} = \frac{C - C _{P}}{C - C _{V}}$

n=CV​CP​​

n=C−CV​C−CP​​

n=C−CV​CP​−C​

n=C−CP​C−CV​​

C=CV​+1−ηR​ ⇒1−n=C−CV​R​ n=1−C−CV​R​=C−CV​C−(CV​+R)​=C−CV​C−CP​​

$n = \frac{C _{P}}{C _{V}}$

$n = \frac{C - C _{P}}{C - C _{V}}$

$n = \frac{C _{P} - C}{C - C _{V}}$

$n = \frac{C - C _{V}}{C - C _{P}}$

$C = C_{V} + \frac{R}{1 - η}$
$\Rightarrow 1 - n = \frac{R}{C - C _{V}}$
$n = 1 - \frac{R}{C - C _{V}} = \frac{C - ( C _{V} + R )}{C - C _{V}} = \frac{C - C _{P}}{C - C _{V}}$