If three moles of monoatomic gas is mixed with two moles of a diatomic gas , the value of adiabatic exponent for the mixture is

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Solution

Q.
If three moles of monoatomic gas $(γ = \frac{5}{3})$ is mixed with two moles of a diatomic gas $(γ = \frac{7}{5})$ , the value of adiabatic exponent $γ$ for the mixture is [2024]

1 1.75

2 1.40

3 1.52

4 1.35

Ans.
(3)

Monoatomic gas $\to 3$ mole

  Diatomic gas $\to 2$ mole

$γ_{m i x} = 1 + \frac{2}{f_{m i n}}$ ....(1)

   $f_{m i x} = \frac{n_{1} f_{1} + n_{2} f_{2}}{n_{1} + n_{2}} = \frac{3 (3) + 2 (5)}{5} = \frac{19}{5}$

   $γ_{m i x} = 1 + \frac{2}{19 / 5} = 1 + \frac{10}{19} = \frac{29}{19}$

   $γ_{m i x} = 1.53$

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