Question

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 491cm3 of air at atmospheric pressure (1.01

Answer 1

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A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm^3 of air at atmospheric pressure (1.01x10^5 Pa ) and a temperature of 27.0*C. At the end of the stroke, the air has been compressed to a volume of 46.2cm^3 and the gauge pressure has increased to 2.72x10^6 Pa

ANS

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

Why is n constant? Because we make no change to the amount of gas molecules (ignore moles of gasoline evaporating, since they are far less than the air).

Why is R constant? Because it is a universal constant for all ideal gasses.

Solve version 1 for n*R:
n*R = P1*V1/T1

Solve version 2 for T2:
T2 = P2*V2/(n*R)

Substitute and simplify:
T2 = T1*P2*V2/(P1*V1)

Caution: ideal gas law equations ONLY work when temperature is in absolute units, and when pressure is absolute pressure.

We had temperatures in Celsius, and before plugging in data, it is crucial to convert to Kelvin.

As for Pressure, at state 2, we know gauge pressure, not absolute pressure.

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)

Data:
T1:=300.15 K; P2g:=2720 kPa; P1:=101 kPa; V2:=46.2 cm^3; V1:=499 cm^3;

Result:
T2 = 776.2 Kelvin

And translated back to Celsius:
T2 = 503.0 Celsius