Discussion Forum

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 (here C_p and C_v are molar specific heat at constant pressure and constant volume respectively)

Answer:

Explanation:

$\triangle Q= \triangle U+\triangle W$

 In the process pVⁿ  = constant, molar heat capacity is given by

$C= \frac{R}{\gamma -1}+\frac{R}{1-n}=C_{v}+\frac{R}{1-n}$

$C-C_{v}= \frac{R}{1-n}$

 $\Rightarrow  1-n=\frac{C_{p}-C_{v}}{C-C_{v}}$

  $\therefore  n= 1-(\frac{C_{p}-C_{v}}{C-C_{v}})$

$\frac{(C-C_{v})-(C_{p}-C_{v})}{C-C_{v}}$

$n=\frac{C-C_{p}}{C-C_{v}}$