Answer to Question #272001 in Molecular Physics | Thermodynamics for dandan

Question

An automobile tire is inflated to 32 psig pressure at 50 F. After being driven the temperature rise to 75F. Determine the final gage pressure assuming the volume remains constant.

Answer 1

Process is isochoric

Ideal Gas Law

$pV=nRT \\ pV=RT \\ \frac{p}{T} = \frac{R}{V} = constant \\ \frac{p_1}{T_1} = \frac{p_2}{T_2} \\ p_2 = \frac{p_1 \times T_2}{T_1} \\ T_2 = 75 \; F = 297 \;K \\ T_1 = 50 \;F = 283 \;K \\ p_2 = \frac{32 \times 297}{283} = 33.58 \;psig$