Question

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.

Answer 1

The pressure is 37.56 atm.

Temperature at the end of adiabatic compression is 825.73 K.

Step-by-step explanation:

Given that

`T_1=20C`

`P_1=1\ atm`

`V_1=800\ cm^3`

`V_2=60\ cm^3`

So r=800/60=13.33

γ=1.4

For process 1-2

`(T_2)/(T_1)=r^(\gamma -1)`

`(T_2)/(273+20)=13.33^(1.4-1)`

`T_2=825.73\ K`

`(P_2)/(P_1)=r^\gamma`

`(P_2)/(1)=13.33^(1.4)`

`P_2=37.56\ atm`

So

The pressure is 37.56 atm.

Temperature at the end of adiabatic compression is 825.73 K.