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

Question

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

Tardigrade Admin · Accepted Answer

For a polytropic process, C=CV+(R/1 - n)⇒ C-CV=(CP - CV/1 - n) ⇒ 1-n=(CP - CV/C - CV) ⇒ n=1-(CP - CV/C - CV)=(C - CP/C - CV) .

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

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

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

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

For a polytropic process,
$C = C_{V} + \frac{R}{1 - n} \Rightarrow C - C_{V} = \frac{C _{P} - C _{V}}{1 - n}$
$\Rightarrow 1 - n = \frac{C _{P} - C _{V}}{C - C _{V}}$
$\Rightarrow n = 1 - \frac{C _{P} - C _{V}}{C - C _{V}} = \frac{C - C _{P}}{C - C _{V}}$ .

n=C−CV​CP​−CV​​

n=C−CP​C−CV​​

n=CV​CP​​

n=C−CV​C−CP​​

For a polytropic process, C=CV​+1−nR​⇒C−CV​=1−nCP​−CV​​ ⇒1−n=C−CV​CP​−CV​​ ⇒n=1−C−CV​CP​−CV​​=C−CV​C−CP​​ .

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

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

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

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

For a polytropic process,
$C = C_{V} + \frac{R}{1 - n} \Rightarrow C - C_{V} = \frac{C _{P} - C _{V}}{1 - n}$
$\Rightarrow 1 - n = \frac{C _{P} - C _{V}}{C - C _{V}}$
$\Rightarrow n = 1 - \frac{C _{P} - C _{V}}{C - C _{V}} = \frac{C - C _{P}}{C - C _{V}}$ .