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Two moles of helium (He) are mixed with ...

Two moles of helium (He) are mixed with four moles of hydrogen `(H_2)`. Find
(a) `(C_(V)` of the mixture
(b) `(C_(P)` of the mixture and
( c) `(gamma) `of the mixture.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Helium is a monoatomic gas.
:. `C_V = 3/2 R, C_P = 5/2 R and gamma = 5/3`
Hydrogen is a diatomic gas.
`:. C_V = 5/2 R` and `C_V = 7/2 R and gamma = 7/5`
(a) `(C_V)` of the mixture
`C_V = (n_1 C_V 1 + n_2 C_(V 2))/ (n_1 + n_2) = ((2)(3/2 R) + 4(5/2 R))/(2 + 4)`
= `(13)/6 R`
(b) `(C_P)` of the mixture
`C_P = C_V + R = (13)/6 R + R`
= `(19)/6 R`.
(c) `gamma` of the mixture
`gamma = (C_p)/(C_V) = ((19//6) R)/((13//6)R)`
= `(19)/(13)`.
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