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Question: One mole of ideal monoatomic gas \((\gamma = 5/3)\) is mixed with one mole of diatomic gas \((\gamma...

One mole of ideal monoatomic gas (γ=5/3)(\gamma = 5/3) is mixed with one mole of diatomic gas (γ=7/5).(\gamma = 7/5). what is γ\gamma for the mixture? γ\gamma denotes the ratio of specific heat at constant pressure, to that at constant volume

A

3/2

B

23/15

C

35/23

D

4/3

Answer

3/2

Explanation

Solution

γmix=μ1γ1γ1−1+μ2γ2γ2−1μ1γ1−1+μ2γ2−1=1×53(53−1)+1×75(75−1)1(53−1)+1(75−1)=32=1.5\gamma_{\text{mix}} = \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}} = \frac{\frac{1 \times \frac{5}{3}}{\left( \frac{5}{3} - 1 \right)} + \frac{1 \times \frac{7}{5}}{\left( \frac{7}{5} - 1 \right)}}{\frac{1}{\left( \frac{5}{3} - 1 \right)} + \frac{1}{\left( \frac{7}{5} - 1 \right)}} = \frac{3}{2} = 1.5