Question

Two moles of helium $\left(He\right)$ are mixed with four moles of hydrogen $\left(H_2\right)$. The molar heat capacity of the mixture at constant pressure is

• A. $\frac{19R}{6}$
• B. $\frac{17R}{6}$
• C. $\frac{15R}{6}$
• D. $\frac{3R}{2}$

Answer 1

The correct option is A $\frac{19R}{6}$

Given,
No. of moles of helium $\left(He\right)=2$
No. of moles of hydrogen $\left(H_2\right)=4$
Since, hydrogen is diatomic and helium is monoatomic.
Therefore,
${\left(C_P\right)}_{H_2}=\frac{7R}{2};{\left(C_P\right)}_{He}=\frac{5R}{2}$
We know that,
$(C_P{)}_{\text{mixture}}=\frac{n_1{C}_{P_1}+n_2{C}_{P_2}}{n_1+n_2}$
$=\frac{2\left(\frac{5R}{2}\right)+4\left(\frac{7R}{2}\right)}{2+4}$
$=\frac{19R}{6}$