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Chemistry Question on Chemical Kinetics

The molar specific heats of an ideal gas at constant pressure and volume are denoted by CP C_P and CVC_V, respectively. If γ=CPCV\gamma = \frac{C_P}{ C_V} and RR is the universal gas constant, then CVC_V is equal to :

A

γR\gamma R

B

1+γ1−γ \frac{1 + \gamma}{1 - \gamma}

C

R(γ−1)\frac{R}{(\gamma - 1)}

D

(γ−1)R\frac{( \gamma - 1)}{R}

Answer

R(γ−1)\frac{R}{(\gamma - 1)}

Explanation

Solution

Using CP−CV=RC_{P}-C_{V}=R ⇒CV(CPCV−1)=R\Rightarrow C_{V}\left(\frac{C_{P}}{C_{V}}-1\right)=R (γ−1)=RCV(\gamma-1)=\frac{R}{C_{V}} (∵CpCV=γ)\left(\because \frac{C_{p}}{C_{V}}=\gamma\right) or CV=R(γ−1)C_{V}=\frac{R}{(\gamma-1)}