A gaseous mixture consists of 16 g of helium (He) and 16 g oxygen `(O_2)`, the ratio `C_P/C_V` of the mixture is = ......

Options

A. 1.4
B. 1.54
C. 1.59
D. 1.62

Answer

D

Explanation

For 16 g He, `n_1=16/4`=4,
For 16 g `O_2, n_2=16/32=1/2`
For mixture of gas,
`C_V=(n_1C_(V1)+n_2C_(V2))/(n_1+n_2)` where, `C_V=f/2 R`
`C_P=(n_1C_(P1)+n_2C_(P2))/(n_1+n_2)` where, `C_P=(f/2+1)R`
For `H_2, f_1=3, n_1=4`, For `O_2, f_2=5, n_2=1/2`
`therfore C_P/C_V=(n_1((f_1)/2+1)R+n_2((f_2)/2+1)R)/(n_1f_1R+n_2(f_2R))`
`=(4(3/2+1)R+1/2(5/2+1)R)/(4(3/2R)+1/2xx5/2R)`
`=(4xx5/2R + 1/2xx7/2R)/(6R+5/4R) =(10R+7/4R)/(6R+5/4R)`
`=(40R + 7R)/(24R+5R)=47/29`=1.62