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  • One mole of a monoatomic gas is mixed with one mole of a diatomic gas <img alt="(\gamma=

One mole of a monoatomic gas(\gamma=5 / 3) is mixed with one mole of a diatomic gas (\gamma=7 / 5). What will be
value of \gamma for the mixture?

Option: 1

1.5


Option: 2

1.54


Option: 3

1.4


Option: 4

1.45


Answers (1)

For a monoatomic gas, \mathrm{C_v=3 R / 2} and for a diatomic gas, \mathrm{C_v=5 R / 2} Since one mole of each gas is mixed together, the \mathrm{C_v} of the mixture will

\mathrm{C_v=\frac{1}{2}\left[\frac{3 R}{2}+\frac{5 R}{2}\right]=2 R}

\mathrm{\text { Now } C_p-C_v=R \text {. Therefore, for the mixture, } C_p=R+C_v=R+2 R=3 R \text {. }}

Hence, the ratio of the specific heats of the mixture is

\mathrm{\gamma=\frac{C_p}{C_v}=\frac{3 R}{2 R}=\frac{3}{2}=1.5}

Posted by

Sumit Saini

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