   # A bicycle tire is filled with air to a pressure of 75 psi at a temperature of 19°C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58°C. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 56E
Textbook Problem
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## A bicycle tire is filled with air to a pressure of 75 psi at a temperature of 19°C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58°C. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire?

Interpretation Introduction

Interpretation: For the given data, the pressure inside the bicycle tire should be determined.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation. For a gas at two conditions, the unknown variable can be determined by knowing the variables that change and remain constant and can be generated an equation for unknown variable from ideal gas equation.

### Explanation of Solution

Explanation

According to ideal gas equation,

PV=nRT

By rearranging the above equation,

PVT=nR

Here for the given dta n is constant and R is a gas constant, for a gas at two conditions the equation can be written as:

P1V1T1=nR=P2V2T2orP1V1T1=P2V2T2

For the given data, for a constant number of moles the equation for final pressure should be

P2=P1V1T2V2T1 (1)

From the ideal gas equation the equation for final pressure for a gas at two conditions can be derived by knowing initial pressure ( P1 ), temperature ( T1 ) and volume ( V1 ) and final volume

( V2 ), temperature ( T2 ). It is the ratio of product of initial volume, pressure and final temperature to the product of initial temperature and final volume

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