Answer to Question #199755 in Mechanics | Relativity for Master j

Question #199755

Air is to be compressed in a diesel engine cylinder. The initial pressure and temperature are 105 kN/m2 and 15 °C respectively and the final pressure is 7 MPa. In order to ignite the fuel charge injected at the end of compression, the temperature required is 1100 °C. Calculate the ratio of the initial to the final volume for this to be possible.


1
Expert's answer
2021-05-30T13:28:44-0400

Initial Pressure, P1=105×103 PaP_1=105\times10^3\space Pa

Final Pressure, P2=7×106 PaP_2=7\times10^{6}\space Pa

Initial Temperature, T1=15°C=288 KT_1=15\degree C=288\space K

Final Temperature, T2=1100°C=1373 KT_2=1100\degree C=1373\space K

Initial Volume =V1=V_1

Final Volume =V2=V_2

P1V1T1=P2V2T2\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}

V1V2=P2×T1P1×T2\dfrac{V_1}{V_2}=\dfrac{P_2\times T_1}{P_1\times T_2}

V1V2=13.98\dfrac{V_1}{V_2}=13.98


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