A mixture needs weighted capacities

A nonreacting ideal mixture contains 2 mol of a monatomic gas and 1 mol of a diatomic gas with translation and rotation active but vibration frozen.

What is the mixture’s γ?

Organize the givens & assumptions

Monatomic amount = 2 mol
Diatomic amount = 1 mol
Constant active modes

Closed fixed amount of ideal gas, constant stated heat capacities, negligible bulk kinetic and gravitational energy changes, and only pressure–volume work. Heat into the gas and work by the gas are positive.

A $\frac75$
B $\frac{17}{11}$
C $\frac{23}{15}$
D $\frac53$

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