One mole of ideal monoatomic gas (\gamma =5/3) is mixed with one mole of diatomic gas (\gamma =7/5) . What is \gamma for the mixture ? \gamma denotes the ratio of specific heat at constant pressure, to that at constant volume.

  • Option 1)

    3/2\;

  • Option 2)

    \; 23/15\;

  • Option 3)

    \; 35/23

  • Option 4)

    \; \; 4/3

 

Answers (1)

As we learnt in 

First law in isobaric process -

\Delta U= n\, C_{v}\Delta T

= n\frac{R}{\gamma -1}\Delta T
 

- wherein

\Delta Q= \Delta U+W

         = n\frac{\gamma \: R}{\gamma -1}\cdot \Delta T

\Delta Q= nC_{p}\: \Delta T

 

 \gamma ^{mix}= \frac{n _{1}C_{P1}+n _{2}C_{P2}}{n _{1}C_{V1}+n _{2}C_{V2}}

n_{1}=1,\ C_{P1}= \frac{\gamma _{1}R}{\gamma _{1}-1}=\frac{7R}{2};\ C_{V1}= \frac{R}{\gamma _{1}-1}=\frac{5R}{2}

n_{2} = 1, C_{P2}= \frac{\gamma _{2}R}{\gamma _{2}-1}=\frac{5R}{2}; C_{V2}= \frac{R}{\gamma _{2}-1}=\frac{3R}{2}

\therefore \gamma ^{mix}=1.5

 


Option 1)

3/2\;

This option is correct.

Option 2)

\; 23/15\;

This option is incorrect.

Option 3)

\; 35/23

This option is incorrect.

Option 4)

\; \; 4/3

This option is incorrect.

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