Chapter 5, Problem 5.20P

Interpretation Introduction

Interpretation:

Given that the pressure in an automobile tire is $2.3\text{0 atm}$ at a temperature of $20.0{}^{\text{o}}\text{C}$. The pressure in the tire if after $10$ miles of driving the temperature of the tire increased to $47.{\text{0 }}^{\text{o}}\text{C}$ should be calculated.

Concept Introduction:

The final pressure of the gas at the varying temperatures can be calculated using Gay-Lussac’s law, which states the relationship between pressure and temperature of the gas.

According to Gay-Lussac’s Law, for the gas held at constant volume, the pressure of a given amount of gas is directly proportional to the temperature of the gas. Mathematically, it is given as.

$P\propto T$.

$\frac{P}{T}=\text{constant}=k$.

We two different sets of temperature and pressure of the gas is considered, the above equation becomes as follows:

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$.

where $P_1$ and $T_1$ are initial pressure and temperature of the gas, while $P_2$ and $T_2$ are final pressure and temperature of the gas.