Answer to Question #104964 in Physics for Nyx

Question

An automobile tire having a temperature of
4.8
◦C (a cold tire on a cold day) is filled to a
gauge pressure of 20 lb/in2.
What would be the gauge pressure in the
tire when its temperature rises to 22◦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

$$\frac{p_1}{T_1}=\frac{p_2}{T_2}$$

$$\frac{p_1^g+p_0}{T_1}=\frac{p_2^g+p_0}{T_2}$$

$$\frac{20+14.7}{4.8+273.15}=\frac{p_2^g+14.7}{22+273.15}$$

$$p_2^g=22.1\frac{lb}{in^2}$$