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Confused! kindly explain, - Thermodynamics - JEE Main

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio C_{P}/C_{V} of the mixture is

  • Option 1)

    1.4\; \;

  • Option 2)

    \; 1.54\;

  • Option 3)

    \; 1.59\;

  • Option 4)

    \; 1.62

 
Answers (1)
121 Views
V Vakul

As we learnt in 

Specific heat in isobaric process -

C_{p}= \left ( \frac{f}{2}+1 \right )R

\gamma^{mix}=\frac{n_{1}C_{p1}+n_{2}C_{p2}}{n_{1}C_{v1}+n_{2}C_{v2}}

 

- wherein

f is degree of freedom

 

\gamma ^{mix} = \frac{n_{1}C_{p1}+n_{2}C_{p2}}{n_{1}C_{v1}+n_{2}C_{v2}}

n_{1} = \frac{16}{4} = 4, C_{v1} = \frac{3R}{2}, C_{p1} = \frac{5R}{2}

n_{2} = \frac{16}{32} = \frac{1}{2}, C_{v2} = \frac{5R}{2}, C_{p2} = \frac{7R}{2}

\gamma ^{mix} = \frac{10R+\frac{7R}{4}}{6R+\frac{5R}{4}}

= \frac{47}{29} = 1.62

 

  

 


Option 1)

1.4\; \;

This option is incorrect.

Option 2)

\; 1.54\;

This option is incorrect.

Option 3)

\; 1.59\;

This option is incorrect.

Option 4)

\; 1.62

This option is correct.

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