A polytropic process for an ideal gas is represented by equation P Vn= constant. If g is ratio of specific heats ((Cp/Cv)), then value of n for which molar heat capacity of the process is negative, is given as:

Question

A polytropic process for an ideal gas is represented by equation P Vn= constant. If g is ratio of specific heats ((Cp/Cv)), then value of n for which molar heat capacity of the process is negative, is given as: (A) &gamma; > n (B) &gamma; > n > 1 (C) n > &gamma; (D) none, as it is not possible

Tardigrade Admin · Accepted Answer

C=(R/&gamma;-1)-(R/n-1) =(R(n-&gamma;)/(n-1)(&gamma;-1)) C is negative if &gamma;>n>1

Q. A polytropic process for an ideal gas is represented by equation $P V^{n} =$ constant. If $g$ is ratio of specific heats $(\frac{C _{p}}{C _{v}})$ , then value of $n$ for which molar heat capacity of the process is negative, is given as:

$γ > n$

$γ > n > 1$

$n > γ$

none, as it is not possible

$C = \frac{R}{γ - 1} - \frac{R}{n - 1}$
$= \frac{R ( n - γ )}{( n - 1 ) ( γ - 1 )}$
$C$ is negative if $γ > n > 1$

Q. A polytropic process for an ideal gas is represented by equation PVn= constant. If g is ratio of specific heats (Cv​Cp​​), then value of n for which molar heat capacity of the process is negative, is given as:

γ>n

γ>n>1

n>γ