A mixture consists of 1 mole of helium ( C_p = 2.5 R , C_V = 1.5 R...

For a mixture of gases, the molar heat capacity at constant volume is given by:

$C_V = \dfrac{n_1 C_{V1} + n_2 C_{V2}}{n_1 + n_2}$

Substituting the given values:

$C_V = \dfrac{1 \times 1.5 R + 1 \times 2.5 R}{1 + 1} = \dfrac{4 R}{2} = 2 R$

The molar heat capacity at constant pressure for the mixture is given by:

$C_p = \dfrac{n_1 C_{p1} + n_2 C_{p2}}{n_1 + n_2}$

Substituting the given values:

$C_p = \dfrac{1 \times 2.5 R + 1 \times 3.5 R}{1 + 1} = \dfrac{6 R}{2} = 3 R$

The ratio of specific heats for the mixture is:

$\gamma = \dfrac{C_p}{C_V} = \dfrac{3 R}{2 R} = 1.5$