Two moles of oxygen are mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is

Options

A. `1.3` R
B. `1.4` R
C. 1.7 R
D. 1.9 R

Answer

A, C

Explanation

Let, for mixture of gases, specific heat at constant volume be `C_(v).`
`C_(v)=(n_(1)(C_(v))_(1)+n_(2)(C_(v))_(2))/(n_(1)+n_(2))`
where, for oxygen,
`C_(v)=(5R)/(2),nn_(1)=2` mol
For helium, `C_(v_(2))=(3R)/(2),n_(2)=8` mol
Therefore,
`C_(v)=((2xx5R)/(2)+8xx(3R)/(2))/(2+8)`
`=(17R)/(10)=1.7R`