1. **State the problem**: We need to calculate the mass of air at the inlet of a chamber given: r = 10:1 (compression ratio), intake pressure $P_1 = 100$ kPa = $100\times10^3$ Pa, intake temperature $T_1 = 27^\circ C = 300$ K (since $27 + 273 = 300$), chamber volume before compression $V_1 = 600$ m³, $\gamma = 1.4$, $C_p = 1.01$ kJ/kg·K, $C_v = 0.718$ kJ/kg·K. 2. **Recall the ideal gas law**: $$ PV = mRT $$ Where $m$ is mass, $R$ is the specific gas constant for air, $P$ is pressure, $V$ is volume, and $T$ is temperature. 3. **Calculate $R$ (specific gas constant for air)**: Given $ C_p = 1.01$ kJ/kg·K = 1010 J/kg·K and $C_v = 0.718$ kJ/kg·K = 718 J/kg·K, $$ R = C_p - C_v = 1010 - 718 = 292 \text{ J/kg·K} $$ 4. **Apply the ideal gas law to find $m$**: $$ m = \frac{P_1 V_1}{R T_1} $$ Substituting values: $$ m = \frac{100000 \times 600}{292 \times 300} $$ 5. **Calculate the mass**: $$ m = \frac{60000000}{87600} \approx 684.93 \text{ kg} $$ **Final answer:** The mass of air at the inlet is approximately **684.93 kg**.