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
P1=13 psiaT1=120 °F=322.039 KV2=V112P_1 = 13 \; psia \\ T_1 = 120 \; °F = 322.039 \; K \\ V_2 = \frac{V_1}{12}P1=13psiaT1=120°F=322.039KV2=12V1
Adiabatic compression
P2P1=(V1V2)γT2T1=(V1V2)γ−1P2=P1×(12)1.4=13×(12)1.4P2=421.499 psiaT2=T1×(V1V2)γ−1=322.039×(12)0.4=870.123 KT2=1106.551 °F≈1010 °F\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 \; °FP1P2=(V2V1)γT1T2=(V2V1)γ−1P2=P1×(12)1.4=13×(12)1.4P2=421.499psiaT2=T1×(V2V1)γ−1=322.039×(12)0.4=870.123KT2=1106.551°F≈1010°F
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