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

Question

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.

Answer 1

Initial Pressure, $P_1=105\times10^3\space Pa$

Final Pressure, $P_2=7\times10^{6}\space Pa$

Initial Temperature, $T_1=15\degree C=288\space K$

Final Temperature, $T_2=1100\degree C=1373\space K$

Initial Volume $=V_1$

Final Volume $=V_2$

$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

$\dfrac{V_1}{V_2}=\dfrac{P_2\times T_1}{P_1\times T_2}$

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