Answer to Question #108109 in Physics for Layla

Question

An automobile tire having a temperature of
0.028◦C (a cold tire on a cold day) is filled to
a gauge pressure of 27 lb/in2
.
What would be the gauge pressure in the
tire when its temperature rises to 32◦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

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

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

$$\frac{27+14.7}{0.028+273.15}=\frac{p_2^g+14.7}{32+273.15}$$

$$p_2^g=31.9\frac{lb}{in^2}$$