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If one mole of a monatomic gas (gamma=5/...

If one mole of a monatomic gas `(gamma=5/3)` is mixed with one mole of a diatomic gas `(gamma=7/5),` the value of gamma for mixture is

A

`1.40`

B

`1.50`

C

`1.53`

D

`3.07`

Text Solution

Verified by Experts

The correct Answer is:
B
`gamma_("mixture")=((n_(1)gamma_(1))/(gamma_(1)-1)+(n_(2)gamma_(2))/(gamma_(2)-1))/((n_(1))/(gamma_(1)-1)+(n_(2))/(gamma_(2)-1))`
Here, `n_(1)=1,gamma_(1)=(5)/(3),n_(2)=1,gamma_(2)=(7)/(5)`
`therefore gamma_("mixture")=((1xx(5)/(3))/([(5)/(3)-1])+(1xx(7)/(5))/([(7)/(5)-1]))/([(1)/((5)/(3)-1)]+[(1)/((7)/(5)-1)])=(3)/(2)=1.5`
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