A sample of $0.50 mol$ of an ideal gas absorbs $727.5 J$ of heat at constant pressure and its temperature rises by $50.0 K$ . Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , find $γ = C_{P} / C_{V}$ of the gas (two decimals).

Numerical answer type, tolerance 0.01.

Answer: 1.4

C_{P} = q_{P} / (n Δ T) = 727.5/ (0.50 \times 50.0) = 29.1 J mo l^{- 1} K^{- 1}

. Then

C_{V} = C_{P} - R = 20.786

, and

γ = 29.1/20.786 = 1.400

, about 1.40, consistent with a diatomic gas.