A common unit for pressure is pounds per square inch (PSI). show that 1 atm = 14

Question

A common unit for pressure is pounds per square inch (PSI). show that 1 atm = 14.7 PSI. An automobile tire is inflated to 28.0 PSI gauge pressure when cold, at 18 C.

A) What will be the pressure if the tire is heated to 32 C by running?

B) What percent of the air in the tire would then have to be let out in order to reduce the pressure to th original 28.0 PSI? assume that the volume of the tire remains constant with temperature. ( A tire gauge measures not the pressure of the air inside but its excess over the external pressure, which is 14.7 PSI.)

Explanation / Answer

1 atm = 760 mm of mercury = 101325 Pa = 101325 N/sq.m
1 atm = 14.7 PSI

1 pound = 0.45 kg
1 sq.inch = 0.0006 sq.m

1 PSI = 0.45 *9.8/0.0006 Pa = 6895 Pa
6895 Pa = 6895/101325 atm = 0.068 atm or 1 atm = 14.7 PSI

A. Assuming ideal behaviour of gas and volume constant,

P1/T1 = P2/T2
or 42.7/291 = P2/305
or P2= 44.75 PSI

Gauge value = 30.05 PSI

B.

To reduce to 28 PSI,
we need to let out 30.05 - 28 = 2.05 PSI
Percentage of air = 2.05/44.75 *100 = 4.58%

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