One of the parameters used to describe automobile engines is the compression ratio, which is the ratio of the volume in the piston-cylinder device in the engine at time1(the maximum volume) to the volume in the piston at time 2 (the minimum volume) as shown in the figure.
a) Assume that the working fluid is air, the pressure at time 1 is 95 kPa, the temperature is 295 K and the compression ratio is 8. Also, assume that air has constant specific heat values as defined at room temperature in table A-2. If the system is adiabatic and the compression process is reversible, determine the final pressure of the air.
b)assuming variable specific heat capacity. Hint: You’ll need to calculate the temperature at time 2 and then use the ideal gas law to find the pressure.
Homework Answers
We know that from ideal gas equation
P1 V1 /T1 = P2 V2 /T2 ➡ T2 = P2V2 T1/P1V1
And from Boil's law
P1V1= P2V2
P1(V1/V2)= P2
P2= 95(8)= 760 kpa
P1 - intial pressure = 95 kpa
V1- initial volume
T1 - initial temperature= 295 k
P2- Final pressure=
V2 - final volume
T2- final temperature
T2= P2V2 T1/P1V1 = (P2 T1/P1)(V2/V1)
T2 = (760 ×295/95) (1/8) = 295 k
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