Question

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one...

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 498 cm3 of air at atmospheric pressure (1.01×105Pa) and a temperature of 27.0 ?C. At the end of the stroke, the air has been compressed to a volume of 46.4 cm3 and the gauge pressure has increased to 2.80×106 Pa . Compute the final temperature.

Construct two versions of the ideal gas law:
P1*V1 = n*R*T1
P2*V2 = n*R*T2

from equation 1
n*R = P1*V1/T1

from equation 2
T2 = P2*V2/(n*R)

Substitute and simplify:
T2 = T1*P2*V2/(P1*V1)
Absolute pressure at state 2 in terms of state 2 gauge pressure (P2g):
P2 = P2g + background pressure
Our background pressure is identical to the pressure at intake state, thus:
P2 = P2g + P1

Thus:
T2 = T1*(P2g + P1)*V2/(P1*V1)

given data
T1=300.15 K

P2g=2800 kPa; P1=101 kPa

V2=46.4 cm3; V1=498 cm3;

T2 =300.15 K *(2800 KPa + 101 KPa)*46.4 cm3/(101 KPa*498 cm3)

T2 = 803.25 Kelvin

And convert into Celsius:
T2 = 530 Celsius

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