Discussion Forum



1)

 If 'Cp' and 'Cv' are molar specific heats of an ideal gas at constant pressure and volume respectively, I f ' $\lambda$ ' is the ratio of two specific heats and ' R'  is universal gas constant then 'Cp' is equal to


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

B) $\gamma $ R

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

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

Answer:

Option A

Explanation:

 Given, that   $\frac{C_{p}}{C_{V}}=\gamma$...........(i)

 as we know that from Mayer's relation  Cp- CV= R

 where R= universal gas constant

 Substitute  the valUe of Cp from the above relation  in Eq.(i) , we get

 $\gamma=\frac{C_{V}}{C_{p}-R}$

 $\gamma(C_{p}-R)=C_{p}$

$\Rightarrow$     $\gamma C_{p}-C_{p}=\gamma R$

   $C_{p}(\gamma-1)=\gamma R$

 $\Rightarrow C_{p}=\frac{\gamma R}{\gamma-1}$

 Hence, Cp  is equal to  $\frac{\gamma R}{\gamma-1}$