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Question: A gaseous mixture consists of 16g of helium and 16g of oxygen. The ratio \(\frac{C_{P}}{C_{V}}\)of t...

A gaseous mixture consists of 16g of helium and 16g of oxygen. The ratio CPCV\frac{C_{P}}{C_{V}}of the mixture is

A

1.4

B

1.54

C

1.59

D

1.62

Answer

1.62

Explanation

Solution

γmixture=μ1γ1γ1−1+μ2γ2γ2−1μ1γ1−1+μ2γ2−1\gamma_{\text{mixture}} = \frac{\frac{\mu_{1}\gamma_{1}}{\gamma_{1} - 1} + \frac{\mu_{2}\gamma_{2}}{\gamma_{2} - 1}}{\frac{\mu_{1}}{\gamma_{1} - 1} + \frac{\mu_{2}}{\gamma_{2} - 1}}

m1 = moles of helium =164=4= \frac{16}{4} = 4

m2 = moles of oxygen

=1632=12= \frac{16}{32} = \frac{1}{2}

Ž gmix =4×5/353−1+1/2×7/575−1453−1+1/275−1=1.62\frac{\frac{4 \times 5/3}{\frac{5}{3} - 1} + \frac{1/2 \times 7/5}{\frac{7}{5} - 1}}{\frac{4}{\frac{5}{3} - 1} + \frac{1/2}{\frac{7}{5} - 1}} = 1.62