Answer to Question #271828 in Molecular Physics | Thermodynamics for MaTMaT

Question

Air is compressed in a diesel engine from an initial pressure of 13 psia and a temperature of 120 F to one-twelfth of its original volume. Calculate the final temperature assuming the compression is adiabatic

Answer 1

$P_1 = 13 \; psia \\ T_1 = 120 \; °F = 322.039 \; K \\ V_2 = \frac{V_1}{12}$

Adiabatic compression

$\frac{P_2}{P_1} = (\frac{V_1}{V_2})^γ \\ \frac{T_2}{T_1} = (\frac{V_1}{V_2})^{γ-1} \\ P_2 = P_1 \times (12)^{1.4} \\ = 13 \times (12)^{1.4} \\ P_2 = 421.499 \; psia \\ T_2 = T_1 \times (\frac{V_1}{V_2})^{γ-1} \\ = 322.039 \times (12)^{0.4} \\ = 870.123 \; K \\ T_2 = 1106.551 \; °F ≈ 1010 \; °F$