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If one mole of a monoatomic gas (gamma=5...

If one mole of a monoatomic gas `(gamma=5//3)` is mixed with one mole of a diatomic gas `(gamma = 7//5)` the value of `gamma` for the 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_1 = 5//3` means gas is monatomic or `C_(V_(1)) = 3/2 R`
`gamma_2 = 7 //5` means gas is diatomic or `C_(V_(2)) = 5//2R`
`C_V` (of the mixture) `= (n_1 C_(V_(1))+ n_2 C_(V_(2)))/(n_1 + n_2) = ((1)(3/2 R)+(1)(5/2)R)/(1+1) = 2R`
`C_p` (of the mixture) `= C_V + R = 3R " "gamma_("mixture") = C_p/C_V = (3R)/(2R) = 1/5`
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