The molar specific heats of an ideal gas at constant pressure and volume are denoted by Cp and Cv, respectively. If

\gamma\frac{\text{C}_{\text{p}}}{\text{C}_{\text{v}}} and R is the universal gas constant, then Cv is equal to:

  • Option 1)

    \gamma\text{R}

  • Option 2)

    \frac{1+\gamma}{1-\gamma}

  • Option 3)

    \frac{\text{R}}{(\gamma-1)}

  • Option 4)

    \frac{(\gamma-1)}{\text{R}}

 

Answers (1)

C_{p}-C_{v} =R ---(1))

and \: r=\frac{C_{p}}{C_{v}}----(2)

Divide equation 91) by Cv we get

=> \frac{C_{p}}{C_{v}}-1=\frac{R}{C_{v}}

=>\frac{R}{C_{v}}=r-1

C_{v}=\frac{R}{r-1}


Option 1)

\gamma\text{R}

Option is Incorrect

Option 2)

\frac{1+\gamma}{1-\gamma}

Option is Incorrect

Option 3)

\frac{\text{R}}{(\gamma-1)}

Option is correct

Option 4)

\frac{(\gamma-1)}{\text{R}}

Option is Incorrect

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