First slide

Heat given

Question

A mixture contains n₁ moles of monoatomic gas and n₂ moles of diatomic gas. If $γ$ = 1.50, the ratio $n_{1} : n_{2}$ :

Easy

A

1 : 1
B

2 : 1
C

1 : 2
D

2 : 3

Solution

$γ_{mixture} = \frac{n_{1} C_{P_{1}} + n_{2} C_{P_{2}}}{n_{1} C_{V_{1}} + n_{2} C_{V_{2}}} \Rightarrow 1.5 = \frac{n_{2} (\frac{5}{2} R) + n_{2} (\frac{7}{2} R)}{n_{1} (\frac{3}{2} R) + n_{2} (\frac{5}{2} R)} \Rightarrow 1.5 = \frac{5 n_{1} + 7 n_{2}}{3 n_{1} + 5 n_{2}} \Rightarrow n_{2} = n_{1}$

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