Air at 20' C in the cylinder of a diesel engine is compressed from an initial pressure of 1 atm and volume of 800 cm3 to 60 cm3. Assume that air behaves as an ideal gas with γ-1.40 and that the compression is adiabatic. Find the final pressure and temperature of the air.

Respuesta :

Answer:

The pressure is 37.56 atm.

Temperature at the end of adiabatic compression is 825.73 K.

Explanation:

Given that

[tex]T_1=20C[/tex]

[tex]P_1=1\ atm[/tex]

[tex]V_1=800\ cm^3[/tex]

[tex]V_2=60\ cm^3[/tex]

So r=800/60=13.33

γ=1.4

For process 1-2

[tex]\dfrac{T_2}{T_1}=r^{\gamma -1}[/tex]

[tex]\dfrac{T_2}{273+20}=13.33^{1.4-1}[/tex]

[tex]T_2=825.73\ K[/tex]

[tex]\dfrac{P_2}{P_1}=r^\gamma[/tex]

[tex]\dfrac{P_2}{1}=13.33^{1.4}[/tex]

[tex]P_2=37.56\ atm[/tex]

So

The pressure is 37.56 atm.

Temperature at the end of adiabatic compression is 825.73 K.

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