Question

1.) What is the absolute pressure of the air in your car's tires, in psi, when your pressure gauge indicates they are inflated to 35.0psi ? Assume you are at sea level.

2.)A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm3 of air at atmospheric pressure

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Answer 1

1)

pressure gauge indicates the pressure difference between two regions. In this case between the inside of the tire and the outside. So it only shows the pressure above atmospheric.

If you want absolute pressure, you need to add the atmospheric pressure as well. For air pressure readings in the atmosphere:

p(absolute) = p(gauge) + p(atmospheric)

2)

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

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