First slide

Intrinsic And Extrinsic Property

Question

3 moles of mono atomic ideal gas are mixed with 2 moles of diatomic ideal gas. Then the ratio of $\frac{C_{P}}{C_{V}}$ of the mixture is

Moderate

A

$\frac{17}{15}$
B

$\frac{29}{19}$
C

$\frac{13}{9}$
D

$\frac{27}{19}$

Solution

(2)
$\begin{array}{l} ' γ_{m}' = \frac{C_{P}}{C_{V}} f o r m o n o a t o m i c g a s = \frac{3 + 2}{3} = \frac{5}{3} C_{p 1} = \frac{5 R}{2}, C_{v 1} = \frac{3 R}{2} \\ ' γ_{d}' = \frac{C_{P}}{C_{V}} f o r d i a a t o m i c g a s = \frac{5 + 2}{5} = \frac{7}{5} C_{p 2} = \frac{7 R}{2}, C_{v 2} = \frac{5 R}{2} \\ γ f o r t h e m i x t u r e \frac{n_{1} C_{p 1} + n_{2} C_{p 2}}{n_{1} C_{v 1} + n_{2} C_{v 2}} = \frac{3 \frac{5 R}{2} + 2 \frac{7 R}{2}}{3 \frac{3 R}{2} + 2 \frac{5 R}{2}} = \frac{15 + 14}{9 + 10} = \frac{29}{19} \end{array}$

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