Question

An automobile tire is inflated to 35 psig at 54 ^oF. After being driven, the temperature rise to 80 ^oF. Determine the final gage pressure assuming volume remains constant

Answer 1

Assuming ideal gas low

Process is Isochoric

$pV=nRT \\ pV = RT \\ \frac{p}{T} = \frac{R}{V} = constant \\ \frac{p_1}{T_1} = \frac{p_2}{V_2} \\ p_2 = \frac{p_1 \times T_2}{T_1} \\ T_1 = 54 =285 \;K \\ T_2 = 80 =299 \;K \\ p_2= \frac{35 \times 299}{285} = 36.72 \;psig$