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  4. 2 moles of helium gas is mixed with 3 moles of hydrogen molecules (taken to be rigid). Find the molar specific heat of the mixture at constant volume. (.R=8.3J/molK.)

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Q. $2$ moles of helium gas is mixed with $3$ moles of hydrogen molecules (taken to be rigid). Find the molar specific heat of the mixture at constant volume. $\left(\right.R=8.3J/molK\left.\right)$

NTA AbhyasNTA Abhyas 2020

Solution:

$\frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}}=\frac{2 \times \frac{3}{2} R + 3 \times \frac{5}{2} R}{2 + 3}=\frac{3 R + 15 \frac{R}{2}}{5}=\left(\frac{2 R}{10}\right)=\frac{21 \times 8 . 3}{10}=17.4J_{mol}K$