Question

Suppose you start your day in Denver, on a cool 10∘C spring day. The local atmospheric pressure is 85 kPa. You fill your car's tires until the gauge shows 210 kPa (about 30 psi). You then drive up to Fairplay, Colorado, where the atmospheric pressure is lower-- 70 kPa --and the temperature drops to 0∘C. When you finish lunch, you check your tire pressure.

Answer 1

Question

What does your gauge read?

Answer:

214.576 kPa

Explanation:

Denver’s temperature in Kelvin= 10+273=283 K

Fairplay’s temperature in Kelvin= 0+273= 273 K

To get absolute pressure, we add atmospheric pressure to gauge pressure

Absolute pressure at Denver=85 +210=295 kPa

Absolute pressure at Fairplay= 70+ Gauge pressure

We know that from ideal gas equation, pressure is directly proportional to temperature hence

where the subscripts D and F denote Denver and Fairly respectively, P and T denote pressure and temperature respectively

$\frac {295}{283}=\frac {P_F}{273}$

$P_F=\frac {295}{283}\times 273=284.576$

Since =70+Gauge pressure, therefore, gauge pressure=284.576-70=214.576 kPa