One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is α 2 4 R J mol K - 1 ; then the value of α will be _____ . (Assume

Question

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is α 2 4 R J mol K - 1 ; then the value of α will be _____ . (Assume that the given diatomic gas has no vibrational mode.)

TestHub · Accepted Answer

Molecular specific heat at constant volume in terms of degrees of freedom is given by $C_{V} = \frac{f}{2} R$
Molecular specific heat of mixture at constant volume is $C_{V} / mix = \frac{n_{1} C_{V_{1}} + n_{2} C_{V_{2}}}{n_{1} + n_{2}}$
$= \frac{1 \times \frac{3 R}{2} + 3 \times \frac{5 R}{2}}{1 + 3}$
$= \frac{9 R}{4} = \frac{α^{2}}{4} R$
$\Rightarrow α = 3$

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