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

$C_{\mathrm{v}}=\frac{\mathrm{n}_{1} \mathrm{C}_{\mathrm{v}_{2}}+\mathrm{n}_{2} \mathrm{C}_{\mathrm{v}_{2}}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$

where, $C_{v}=\frac{f}{2} R, f$ is degree of freedom

and $C_{p}=\frac{n_{1} C_{p_{1}}+n_{2} C_{p_{2}}}{n_{1}+n_{2}}$

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

For helium : $n_{1}=4, f=3$

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

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

Standard 11

Physics

Heat is supplied to a di-atomic gas at constant pressure. The ratio of $\Delta Q:\Delta U:\Delta W$ is

normal

Two containers of equal volume contain the same gas at pressures ${P_1}$ and ${P_2}$ and absolute temperatures ${T_1}$ and ${T_2}$ respectively. On joining the vessels, the gas reaches a common pressure $P$ and common temperature $T.$ The ratio $P/T$ is equal to

normal

The amount of heat energy required to raise the temperature of $1\, g$ of Helium at $NTP,$ from $T_1\, K$ to $T_2\, K$ is

normal

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normal

$P-V$ plots for two gases during adiabatic processes are shown in the figure. Plots $1$ and $2$ should correspond respectively to

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

Solution

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