   Chapter 10, Problem 62AP

Chapter
Section
Textbook Problem

Before beginning a long trip on a hot day, a driver inflates an automobile tire to a gauge pressure of 1.80 atm at 300. K. At the end of the trip, the gauge pressure has increased to 2.20 atm. (a) Assuming the volume has remained constant, what is the temperature of the air inside the tire? (b) What percentage of the original mass of air in the tire should be released so the pressure returns to its original value? Assume the temperature remains at the value found in part (a) and the volume of the tire remains constant as air is released.

(a)

To determine
The temperature of air inside the tire.

Explanation

Given info: The initial gauge pressure is 1.80 atm. The final gauge pressure is 2.20 atm. The initial temperature is 300 K.

At constant volume,

P2P1=T2T1 (I)

• P1 and P2 are the initial and final absolute pressures.
• T1 and T2 are the initial and final temperatures.

The initial gauge pressure is,

P1=(Pa+1.80)atm (II)

• Pa is the atmospheric pressure.

The final gauge pressure is,

P2=(Pa+2.20)atm (III)

• Pa is the atmospheric pressure.

Substitute Equations (II) and (III) in (I) and re-arrange to get T2

(b)

To determine
The percentage of mass of air that should be released.

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