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  4. Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat (in J/mol K) of mixture at constant volume? (R=8.3 J/mol K)

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Q. Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat (in $J/mol \,K)$ of mixture at constant volume? $(R=8.3 J/mol\,K)$

Kinetic Theory

Solution:

$\left[C_{v}\right]_{min} = \frac{n_{1}\left[C_{v_1}\right]+n_{2}\left[C_{v_2}\right]}{n_{1}+n_{2}}$
$=\left[\frac{2\times\frac{3R}{2}+3\times\frac{5R}{2}}{2+3}\right]$
$=2.1\,R $
$=2.1\times8.3$
$=17.4\, J /mol -K$