Air (γ = 1.40) at 1.0 × 10⁵ Pa and 290 K is squeezed quickly to 1/12 of its volume…

Step 1. Temperature. $T_2 = 290\ \text{K} \times 12^{0.40} = 784\ \text{K}$, which is $510\ ^\circ\text{C}$.

Step 2. Pressure. $p_2 = 1.0 \times 10^{5}\ \text{Pa} \times 12^{1.40} = 3.24 \times 10^{6}\ \text{Pa}$.