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A gaseous mixture consists of 16g of hel...

A gaseous mixture consists of 16g of helium and 16 g of oxygen. The ratio `(C_p)/(C_v)` of the mixture is

A

1.4

B

1.54

C

1.59

D

1.62

Text Solution

Verified by Experts

The correct Answer is:
D
For 16 g of helium, `n_(1)=(16)/(4)=4`
For 16 g of oxgyen, `n_(2)=(16)/(32)=(1)/(2)`
For mixture of gases,
`C_(V)=(n_(1)C_(V_(1))+n_(2)C_(V_(2)))/(n_(1)+n_(2))" where "C_(V)=(f)/(2)R`
`C_(P)=(n_(1)C_(P_(1))+n_(2)C_(P_(2)))/(n_(1)+n_(2))" where "C_(P)=((f)/(2)+1)R`
For helium, `f_(1)=3,n_(1)=4`. For oxygen, `f_(2)=5,n_(2)=(1)/(5)`
`therefore (C_(P))/(C_(V))=((4xx(5)/(2)R)+((1)/(2)xx(7)/(2)R))/((4xx(3)/(2)R)+((1)/(2)xx(5)/(2)R))=(47)/(29)=1.62`
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