Answer to Question #106384 in Molecular Physics | Thermodynamics for Ashley Torres

Question

An automobile tire having a temperature of 7.1◦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 38◦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

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

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

$$\frac{26+14.7}{7.1+273.15}=\frac{p_2^g+14.7}{38+273.15}$$

$$p_2^g=30.5\frac{lb}{in^2}$$