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Equal volumes of two monoatomic gases, A and B, at same temperature and pressure are mixed. The ratio of specific heats \left ( C_{p/C_{v}} \right ) of the mixture will be:

  • Option 1)

    0.83

  • Option 2)

    1.50

  • Option 3)

    3.3

  • Option 4)

    1.67

 

Answers (1)

 

Work done in adiabatic process -

W= \frac{P_{2}V_{2}-P_{1}V_{1}}{\gamma -1}

 

- wherein

\gamma = \frac{C_{P}}{C_{V}}

 

 C_{p}^{mix}=n_{1}Cp_{1}+n_{2}Cp_{2}\\ C_{v}^{mix}=n_{1}Cv_{1}+n_{2}Cv_{2}\\ C_{v1}=\frac{fR}{2}=\frac{R}{r-1}=\frac{3R}{2}.,C_{v2}=\frac{fR}{2}=\frac{3R}{2}\\ C_{p1}=C_{v1}+R=\frac{5R}{2},C_{p2}=\frac{5R}{2}

n_{1}=n_{2}=n\\ C_{v}^{mix}=n.\frac{3R}{2}+n.\frac{3R}{2}=3nR\\ C_{p}^{mix}=n.\frac{5R}{2}+n.\frac{5R}{2}=5nR\\

V^{mix}=\frac{C_{p}^{mix}}{C_{v}^{mix}}=\frac{5}{3}=1.67


Option 1)

0.83

This option is incorrect 

Option 2)

1.50

This option is incorrect 

Option 3)

3.3

This option is incorrect 

Option 4)

1.67

This option is correct 

Posted by

Vakul

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