# One mole of mono atomic gas (γ = 5/3) is mixed with one mole of diatomic gas (γ = 7/5) what will be the value of γ for the mixture? Option 1) 1.5 Option 2) 2.5 Option 3) 1.0 Option 4) 2.0

P Plabita

As we learnt in

Specific heat in isobaric process -

$C_{p}= \left ( \frac{f}{2}+1 \right )R$

$\gamma^{mix}=\frac{n_{1}C_{p1}+n_{2}C_{p2}}{n_{1}C_{v1}+n_{2}C_{v2}}$

- wherein

$f$ is degree of freedom

$\gamma ^{mix}=\frac{n_1C_{p_1} +n_2C_{p_2}}{n_1C_{v_1}+n_2C_{v_2}}$

$C_{v_1} =\frac{3R}{2}, Cp_1=\frac{5R}{2}, n_1=1$

$C_{v_2} =\frac{5R}{2}, Cp_2=\frac{7R}{2}, \:n_2=1$

$\gamma ^{mix}= \frac{5R/2 + 7R/2}{3R/2+5R/2}=\frac{6R}{4R}=1.5$

Option 1)

1.5

Correct

Option 2)

2.5

Incorrect

Option 3)

1.0

Incorrect

Option 4)

2.0

Incorrect

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