Two moles of helium gas is mixed with three moles of hydrogen...

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume?

\left(R = 8.3J / molK\right)

Options

A $17.4J / molK$
B $19.7J / molK$
C $15.7J / molK$
D $21.6J / molK$

Correct answer

A. $17.4J / molK$

Step-by-step solution

{\left({C}_{v}\right)}_{mix} = \dfrac{{n}_{1}{C}_{{v}_{1}} + {n}_{2}{C}_{{v}_{2}}}{{n}_{1} + {n}_{2}} = \dfrac{2\left(\dfrac{3}{2}R\right) + 3\left(\dfrac{5}{2}R\right)}{2 + 3}

= \dfrac{3R + \dfrac{15}{2}R}{5} = \dfrac{21}{10}R = 17.4J / molK

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