A vessel contains 1 mole of O2 and 1 mole of He- The value of - of the mixture is

Γ_mix=C_p mix/C_v mix C_mix=n_1 C_1+n_2 C_2/n_1+n_2=C_1+C_2/2 C_v_mix =C_v_1+C_v_2/2=(5/2+3/2) R/2=2 R C_p_mix=C_p_1+C_p_2/2=(7/2+5/2) R/2=3 R γ_mi x=C_p_m i ...

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Byju's Answer

Standard XII

Physics

Specific Heat Capacity

A vessel cont...

Question

A vessel contains $1$ mole of $O_{2}$ and $1$ mole of $H e$ . The value of $γ$ of the mixture is

1.4

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1.5

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1.53

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None

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Solution

The correct option is B $1.5$
$γ_{mix} = \frac{C_{p m i x}}{C_{v m i x}}$

$C_{mix} = \frac{n_{1} C_{1} + n_{2} C_{2}}{n_{1} + n_{2}} = \frac{C_{1} + C_{2}}{2}$

$C_{v_{m i x}} = \frac{C_{v_{1}} + C_{v_{2}}}{2} = \frac{(\frac{5}{2} + \frac{3}{2}) R}{2} = 2 R$
$C_{p_{m i x}} = \frac{C_{p_{1}} + C_{p_{2}}}{2} = \frac{(\frac{7}{2} + \frac{5}{2}) R}{2} = 3 R$
$γ_{m i x} = \frac{C_{p_{m i x}}}{C_{v_{m i x}}} = \frac{3 R}{2 R} = 1.5$

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