When the temperature of an automobile tire is 20°C, the pressure in the tire rea

Question

When the temperature of an automobile tire is 20°C, the pressure in the tire reads 33 psi on a tire gauge. (the gauge measures the difference between the pressures inside and outside the tire.) What is the pressure when the tire heats up to 38°C while driving? You may assume that the volume of the tire remains the same and that atmospheric pressure is a steady 14 psi. When the temperature of an automobile tire is 20°C, the pressure in the tire reads 33 psi on a tire gauge. (the gauge measures the difference between the pressures inside and outside the tire.) What is the pressure when the tire heats up to 38°C while driving? You may assume that the volume of the tire remains the same and that atmospheric pressure is a steady 14 psi.

Explanation / Answer

Since tire is consisting air therefore we assume it as ideal gas
Now
PV = mRT
33V = mR(20+273)
V/mR = (20+273)/33 ----------(1)
Now for second condition
PV = mR(38+273)
V/mR = (38+273)/P -------------(2)
Equating 1 and 2
(38+273)/P = (20+273)/33
P = 35.027 psi

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