A gaseous mixture consists of 16,g of helium and 16,g of oxygen. ratio (Cₚ/ Cᵥ) of mixture is

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12.Kinetic Theory of Gases

normal

A gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/ C_v)$ of the mixture is

$1.4$

$1.54$

$1.59$

$1.62$

Solution

For mixture of gases $:$

$\gamma=\frac{\mathrm{n}_{1} \mathrm{Cp}_{1}+\mathrm{n}_{2} \mathrm{Cp}_{2}}{\mathrm{n}_{1} \mathrm{Cv}_{1}+\mathrm{n}_{2} \mathrm{Cv}_{2}}$

$C_{v}=\frac{f R}{2}$

where, $\mathrm{C}_{\mathrm{p}}=\left(1+\frac{\mathrm{f}}{2}\right) \mathrm{R}$

For helium $: \mathrm{n}_{1}=4, \mathrm{f}=3$

For oxygen $: \mathrm{n}_{2}=\frac{1}{2}, \mathrm{f}=5$

$\therefore \frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4 \times \frac{5 \mathrm{R}}{2}+\frac{1}{2} \times \frac{7 \mathrm{R}}{2}}{4 \times \frac{3 \mathrm{R}}{2}+\frac{1}{2} \times \frac{5 \mathrm{R}}{2}}=\frac{47}{29}=1.62$

Standard 11

Physics

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A gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/ C_v)$ of the mixture is

Solution

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