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One mole of ideal monoatomic gas (gamma=...

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

A

`3//2`

B

`2//5`

C

`2//7`

D

`4//7`

Text Solution

Verified by Experts

The correct Answer is:
A
`gamma` for mixture
`gamma_("mix")=((n_1 gamma_1)/(gamma_1 -1)+(n_2 gamma_2)/(gamma_2-1))/((n_1)/(gamma_1-1)+(n_2)/(gamma_2-1))=(n_1(C_V)_1+n_2(C_V)_2)/((C_V)_1+(C_V)_2)`
`((1xx5/3)/(5/3-1)+(1xx7/5)/(7/5-1))/((1)/((5/3-1))+(1)/((7/5-1))) = 3/2 =1.5`
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