Answer to Question #187651 in Mechanics | Relativity for esteban alvarado

Question

An automobile tire having a temperature of 7.9 ◦C (a cold tire on a cold day) is filled to a gauge pressure of 24 lb/in2 . What would be the gauge pressure in the tire when its temperature rises to 26◦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

At constant volume,

$\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}$

$P_2=T_2\times\dfrac{P_1}{T_2}$

$P_2=(273+7.9)\times\dfrac{(24+14.7)}{(26+273)}$

$P_2=36.35\space lb/m^2$

Gauge Pressure in the tire, $P_g=36.35-14.7=21.65\space lb/m^2$