One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of mixture at constant volume is α24R J/mol‐K ; then the value of α will be _____. (Assume that the given diatomic gas has no vibration mode).

(CV)mix of two mixed is given as, (CV)mix=n1CV1+n2CV2n1+n2=1.3R2+3.5R21+3=9R4=α24R⇒α=3

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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of mixture at constant volume is $\frac{α^{2}}{4} R J / m o l ‐ K$ ; then the value of $α$ will be _____. (Assume that the given diatomic gas has no vibration mode).

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answer is 3.

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Detailed Solution

${(C_{V})}_{m i x}$ of two mixed is given as,

${(C_{V})}_{m i x} = \frac{n_{1} C_{V_{1}} + n_{2} C_{V_{2}}}{n_{1} + n_{2}} = \frac{1. \frac{3 R}{2} + 3. \frac{5 R}{2}}{1 + 3} = \frac{9 R}{4} = \frac{α^{2}}{4} R$

$\Rightarrow α = 3$

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