Question

An automobile tire having a temperature of −1.5 ◦C (a cold tire on a cold day) is filled to a gauge pressure of 26 lb/in2 . What would be the gauge pressure in the tire when its temperature rises to 40◦C? For simplicity, assume that the volume of the tire remains constant, that the air does not leak out and that the atmospheric pressure remains constant at 14.7 lb/in2 . Answer in units of lb/in2 .

Answer 1

Answer:$32.22\ lb/in^2$

Explanation:

Given

Temperature on the hot day $T_i=-1.5^{\circ} C\approx 271.5\ K$

Gauge Pressure $P_i=26\ lb/in^2$

When Temperature rises to $T_f=40^{\circ}C\approx 313\ K$ on a hot day then

absolute pressure  is let say $P_f$

Using ideal gas equation we can write

$\Rightarrow \frac{PV}{T}=constant$

as volume is constant therefore

$\Rightarrow \frac{P}{T}=constant$

$\Rightarrow \frac{26+14.7}{271.5}=\frac{P_f}{313}$

$\Rightarrow P_f=46.92\ lb/in^2$

Gauge Pressure is given by

$\Rightarrow 46.92-14.7=32.22\ lb/in^2$