Discussion Forum



1)

The molar specific heat of an ideal gas at constant pressure and constant volume is CP and CV respectively. If R is the universal gas constant and the ratio of CP TO CV is  $\gamma$, then CV

 


A) $\frac{1-\gamma}{1+\gamma}$

B) $\frac{1+\gamma}{1-\gamma}$

C) $\frac{\gamma-1}{R}$

D) $\frac{R}{\gamma-1}$

Answer:

Option D

Explanation:

According to Mayer formula ,

   Cp  -Cv  = R  .....(i)

 Where, Cp = specific heat at constant pressure,

 CV = specific heat at constant  volume

 and R= gas constant

  Now, $\gamma= \frac{C_{p}}{C_{v}}$

 $\Rightarrow C_{p}=\gamma C_{v}$            ............(ii)

 From  eqs,(i) and (ii) , we get

 $\Rightarrow \gamma C_{v}- C_{v}=R\Rightarrow  C_{v}(\gamma-1)=R$

 $\Rightarrow $   $ C_{v}= \frac{R}{(\gamma-1)}$