Question

A mixture contains 1 mode of helium $C_p$ = 2.5 R, $C_v$ = 1.5 R) and 1 a mole of hydrigen $(C_p$ = 3.5 R, $C_v$ = 2.5 R) Calculate the values of $C_p$ $C_v$ Calculate the values of $C_p{C}_v$ and $\gamma$ for the mixture.

Answer 1

$C{p}^{\prime }=2.5RC{p}^{\prime }=3.5R$

$C{v}^{\prime }=1.5RC{v}^{\prime }=2.5R$

$n_1=n_2=1mol,$

$[n_1+n_2]CvaT=n_{1}CvaT+n_2{C}^{\prime }vaT$

$\Rightarrow Cv=\frac{n_{1}Cv+n_2{C}^{\prime }v}{n_2+n_2}$

= $\frac{1.5R+2.5R}{2}=2R$

Cp = Cv +R = 2R + R = 3R\)

$\gamma =\frac{Cp}{Cv}=\frac{3R}{2R}$ = 1.5